Séminaire
Rencontres statistiques
FREULON Paul (EPFL)
Le 06/01/2025
De 13:30 à 14:30
Titre : Weights estimation in mixture models with entropic optimal transport.
Résumé : While optimal transport allows to compare probability measures with different structures, its computational cost has limited its use in practice. To reduce the algorithmic cost, M.Cuturi proposed in 2013 to regularize the optimal transport problem with the addition of an entropic penalty on the transport plan. The solution of this regularized minimization problem, called entropic optimal transport, defines an alternative way of comparing probability measures. In this talk, through the study of a mixture model parameterized by its weights, I will discuss the statistical effect of regularizing the transport plan. For a chosen regularization parameter, the estimator we consider is defined as the minimum of loss function involving the entropic optimal transport cost. In this framework, we have a collection of estimators, where each weights estimator corresponds to a fixed regularization parameter. Of particular interest for us will be the impact of this regularization parameter on the performance of a weights estimators. We derive upper bounds on the expected excess risks of the estimators considered. From these results we derive an automatic choice of the regularization parameter. As a by product of our analysis, we also propose to automatically choose the number of iterations for the algorithm used to approximate the entropic optimal transport. This talk is based on the preprint https://arxiv.org/abs/2210.06934 ; which is a joint work with Jérémie Bigot, Boris Hejblum and Arthur Leclaire.
Salle : Abis
Colloque
Colloquium du CEREMADE
SERFATY Sylvia (Sorbonne Université)
Le 07/01/2025
De 15:30 à 16:30
Titre : Coulomb systems
Résumé : We are interested in the statistical mechanics and dynamics of large systems of interacting Coulomb or Riesz particles. This is motivated by vortices, quantum and statistical mechanical models, approximation theory, and random matrix models. The mean-field behavior of these systems will be discussed, as well as their microscopic behavior as a function of temperature, which leads in particular to questions of crystallization.
Salle : A709
Séminaire
Séminaire des jeunes chercheurs
MEDINA RODRIGUEZ Richard (CEREMADE)
Le 09/01/2025
De 17:00 à 18:00
Titre : Brief introduction to the Boltzmann equation: well-posedness and long-time behavior in the torus
Résumé : The Boltzmann equation models a system of moving particles which interact through collisions, that we will assume in this talk to be elastic and instantaneous. In this talk we will present the theory of well-posedness and long-time behavior for this equation in the torus. First we will introduce the model and the physical relevance of the different operators, then we will present the expected equilibrium and the linearized equation around such equilibrium. We will introduce then the concept of hypocoercivity for the linearized Boltzmann operator in order to obtain a constructive decay estimate in a suitable functional space. Using the Duhamel formula we will relate the previous functional space with a weighted $L^\infty$ space, which is where we can properly control the non-linear Boltzmann collision operator. We will conclude by constructing solutions for the fully non-linear Boltzmann equation in the perturbative regime by providing a construcitve rate of decay to equilibrium.
Salle : A707
Séminaire
Rencontres statistiques
MEAH Iqraa (CRESS)
Le 20/01/2025
De 16:00 à 18:00
Titre : Evaluating the effect of lung transplantation: a case study in sequential emulated trials with time-dependent matching
Résumé : Lung transplantation has long been a critical intervention to extend the lifespan of individuals diagnosed with cystic fibrosis. As transplant assignment cannot be randomized, evaluating treatment effectiveness relies on observational data. Such data, e.g., provided by the United Network for Organ Sharing (UNOS), are a valuable source to emulate a target trial. The latter is a popular methodology to investigate causal relations using observational data that inherently contain bias. Sources of bias include confounding bias due to non-random treatment assignment and censoring bias in time-to-event analyses. Moreover, if the methodology of emulated trial is not carefully implemented, additional biases, such as immortal time bias, may be introduced, further complicating the estimation of treatment effects. In this work, we use the UNOS data as a case study to develop a methodological framework for emulating target trials in the context of lung transplantation. We address the challenges associated with each type of bias, leading us to a sequence of target trials that incorporate time-dependent matching on confounders. We also discuss the theoretical aspects we aim to explore next in this study design to close some gaps in the literature.
Salle : Salle Abis
Séminaire
Séminaire Analyse-Probabilités
LEBLÉ Thomas (MAP5)
Le 21/01/2025
De 09:00 à 09:00
Titre : Flot gradient de l'énergie libre en volume infini pour des systèmes de spins continus
Résumé : On considère un réseau infini de spins à valeurs dans une variété compacte lisse et ayant entre eux des interactions à courte portée. On construit le flot gradient de l'énergie libre associée en volume infini, à l'aide d'une adaptation de l'approche, introduite par Jordan, Kinderlehrer et Otto, consistant à prendre la limite d'une descente de gradient discrète dans l'espace de Wasserstein. On prouve que les trajectoires du flot gradient et celles de la loi des spins sous la dynamique de Langevin suramortie satisfont à la même hiérarchie d'équations de Fokker-Planck. On obtient la régularité des solutions faibles, et on montre une "Evolution Variational Inequality" pour les solutions régulières, ce qui implique l'unicité. En particulier, les trajectoires du flot gradient coïncident avec celles obtenues par la dynamique de Langevin. Travail en commun avec Ronan Herry (Rennes).
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
TABOADA Roméo (Université Paris-Saclay)
Le 23/01/2025
De 17:00 à 18:00
Titre : Exponential energy decay for wave equations
Résumé : Stabilization is one of the main concerns in control theory : its goal is to bring back perturbed systems to equilibrium states. In this talk, we will study the dampening of a sound using acoustic foam. We will show that, despite being a problem about wave mechanics, its behaviour is actually ruled by geometrical optics. After showing this equivalence, we will see the fundamental role played by resolvent estimates, hinting at a method that can be used in many other fields where "scattering" is involved : quantum mechanics, general relativty, dynamical systems or quantum chemistry.
Salle : A707
Séminaire
Séminaire Analyse-Probabilités
VILLANI Cedric (IHES)
Le 28/01/2025
De 10:30 à 11:30
Titre : Information de Fisher et régularité pour l'équation de Boltzmann
Résumé : Importée par Henry P. McKean en 1966 en théorie cinétique des gaz, l'information de Fisher a joué un rôle clé dans l'étude de la convergence vers l'équilibre en temps grand, et des limites en grand nombre de particules. En 2024, la découverte surprise de sa monotonie en temps le long de l'équation de Boltzmann spatialement homogène, bien plus largement que le cas particulier maxwellien, a permis de résoudre le problème ouvert, identifié de longue date, de la régularité pour des noyaux très singuliers (potentiels très mous), ouvrant finalement la voie à la complétion du programme sur l'équation spatialement homogène, inauguré par Carleman il y a un siècle. C'est un travail en collaboration avec Cyril Imbert et Luis Silvestre, inspiré par l'étude de Nestor Guillen et Luis Silvestre sur l'équation de Landau-Coulomb. Les liens entre théorie collisionnelle des gaz et inégalité de Sobolev logarithmique y apparaissent bien plus forts que précédemment.
Salle : A709
Séminaire
Séminaire des jeunes chercheurs
RAKOTO ENDOR Faniriana (CEREMADE)
Le 30/01/2025
De 17:00 à 18:00
Titre : Benign landscape for Burer-Monteiro factorizations of MaxCut-type semidefinite programs
Résumé : We consider MaxCut-type semidefinite programs (SDP) which admit a low rank solution. To numerically leverage the low rank hypothesis, a standard algorithmic approach is the Burer-Monteiro factorization, which allows to significantly reduce the dimensionality of the problem at the cost of its convexity. We give a sharp condition on the conditioning of the Laplacian matrix associated with the SDP under which any second-order critical point of the non-convex prob- lem is a global minimizer. By applying our theorem, we improve on recent results about the correctness of the Burer-Monteiro approach on Z2 synchronization problems.
Salle : A707
Séminaire
Rencontres statistiques
AKHAVAN Arya (Oxford)
Le 03/02/2025
De 16:00 à 18:00
Titre : A conversion theorem and minimax optimality for continuum contextual bandits
Résumé : I will talk about the contextual continuum bandits problem, where the learner sequentially receives a side information vector and has to choose an action in a convex set, minimizing a function associated with the context. The goal is to minimize all the underlying functions for the received contexts, leading to a dynamic (contextual) notion of regret, which is stronger than the standard static regret. Assuming that the objective functions are Hölder continuous with respect to the contexts, I will show that any algorithm achieving a sub-linear static regret can be extended to achieve a sub-linear dynamic regret. I will also discuss the case of strongly convex and smooth functions when the observations are noisy. Inspired by the interior point method and employing self-concordant barriers, I will talk about our algorithm achieving a sub-linear dynamic regret. Lastly, I present a minimax lower bound, implying two key facts. First, no algorithm can achieve sub-linear dynamic regret over functions that are not continuous with respect to the context. Second, for strongly convex and smooth functions, the algorithm that we propose achieves the minimax optimal rate, up to a logarithmic factor, of dynamic regret as a function of the number of queries.
Salle : Dbis
Colloque
Colloquium du CEREMADE
DALIBARD Anne-Laure (Sorbonne Université)
Le 04/02/2025
De 15:30 à 16:30
Titre : Stationary boundary layers in viscous incompressible fluids
Résumé : When a fluid with small viscosity flows around an obstacle, a zone of small width is usually created in the vicinity of the wall. In this region, called « boundary layer », the velocity of the fluid changes abruptly. The study of fluid boundary layers has been an object of intense research over the past century. In this talk, we will focus on the stationary 2d Prandtl system, which was derived in 1905 by Ludwig Prandtl. We will present a review of results describing the flow in different regimes: without recirculation (i.e. when the tangential velocity close to the wall has the same sign as the velocity far from the obstacle); in the vicinity of the « separation point »; and with a recirculation bubble, i.e. when the tangential velocity changes sign.
Salle : A709
Séminaire
Séminaire des jeunes chercheurs
SOTNIKOV Dimitri (Ecole Polytechnique, CMAP)
Le 06/02/2025
De 17:00 à 18:00
Titre : Heath–Jarrow–Morton meet lifted Heston in energy markets for joint historical and implied calibration
Résumé : In energy markets, joint historical and implied calibration is of paramount importance for practitioners yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from the option market. We address this crucial problem with a parsimonious multiplicative multi-factor Heath-Jarrow-Morton (HJM) model for forward curves, combined with a stochastic volatility factor coming from the Lifted Heston model. We develop a sequential fast calibration procedure leveraging the Kemna-Vorst approximation of futures contracts: (i) historical correlations and the Variance Swap (VS) volatility term structure are captured through Level, Slope, and Curvature factors, (ii) the VS volatility term structure can then be corrected for a perfect match via a fixed-point algorithm, (iii) implied volatility smiles are calibrated using Fourier-based techniques. Our model displays remarkable joint historical and implied calibration fits - to both German power and TTF gas markets - and enables realistic interpolation within the implied volatility hypercube. This is joint work with Eduardo Abi Jaber, Soukaïna Bruneau, Nathan De Carvalho, and Laurent Tur.
Salle : A707
Séminaire
Séminaire Analyse-Probabilités
LATOCCA Mickaël (Evry)
Le 11/02/2025
De 10:30 à 11:30
Titre : Non-invariance de mesures gaussiennes pour le flot d'Euler 2D
Résumé : L'objectif principal est d'exposer un résultat obtenu en collaboration avec Jacob Bedrossian (UCLA) qui prouve essentiellement que les mesures gaussiennes régulières ne sont pas invariantes par le flot de l'équation d'Euler bidimensionnelle. Je commencerai par motiver l'étude des mesures invariantes pour l'équation d'Euler ainsi que leur lien avec des questions de croissance de normes en temps long. J'exposerai ensuite la stratégie élémentaire que nous avons employée pour répondre partiellement à la question posée et, si le temps le permet, je donnerai quelques pistes que nous envisageons pour la suite de ce projet.
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
PHAM Kim Anh (CEREMADE)
Le 13/02/2025
De 17:00 à 18:00
Titre : Introduction to Stochastic Optimal Control under Constraints in Finance
Résumé : Among the various subfields of Financial Mathematics, Stochastic Optimal Control under Constraints (SOCC) answers specifically to the question of portfolio optimization while accounting for the stochastic nature of the financial markets and the restrictions imposed on the portfolio management (by regulators, for example). This presentation aims to serve as an introduction to SOCC by blending its theoretical aspects with practical applications and numerical methods. In particular, we will look at (1) a motivating example from Life Insurance, (2) Dynamic Programming Principle as the core of SOCC, and (3) some applications of Deep Learning for numerical estimation of the optimal controls.
Salle : A707
Séminaire
Rencontres statistiques
MARANDON Ariane ()
Le 17/02/2025
De 13:30 à 14:30
Titre :
Résumé :
Salle : Abis
Séminaire
Séminaire Analyse-Probabilités
ZEITOUNI Ofer (Weizmann Institute of Science)
Le 18/02/2025
De 10:30 à 11:30
Titre : Voting models and tightness for a family of recursion equations
Résumé : We consider recursion equations of the form u_{n+1}(x)=Q[u_n](x), n≥1, x∈R, with a non-local operator Q[u](x)=g(u∗q), where g is a polynomial, satisfying g(0)=0, g(1)=1, g((0,1))⊆(0,1), and q is a (compactly supported) probability density with ∗ denoting convolution. These are discrete analogues of KPP type equations with general (polynomial) nonlinear ties. Motivated by a line of works for nonlinear PDEs initiated by Etheridge, Freeman and Penington (2017), we show that for general g, a probabilistic model based on branching random walk can be given to the solution of the recursion, while in case g is also strictly monotone, a probabilistic threshold-based model can be given. In the latter case, we provide a conditional tightness result. We analyze in detail the bistable case and prove for it convergence of the solution shifted around a linear in n centering. Joint work with Xaver Kriechbaum and Lenya Ryzhik
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
RAMEH Ons (Université Paris-Cité)
Le 20/02/2025
De 17:00 à 18:00
Titre : Autour du phénomène de Cut-off pour des systèmes de particules
Résumé : Considérons un système de particules aléatoires. quand peut-on dire qu'il est proche de l'équilibre ? Parfois, le système atteint rapidement l'équilibre de manière abrupte, ce que l'on qualifie de phénomène de cut-off. Le but de l'exposé est de présenter ce phénomène et d'expliquer quels renseignements fournit le comportement macroscopique d'un système sur le temps de mélange.
Salle : A707
Séminaire
Séminaire des jeunes chercheurs
ZARHALI Othmane (CEREMADE)
Le 27/02/2025
De 17:00 à 18:00
Titre : From rough to multifractal volatility: Topics around the Log S-fBM model
Résumé : The Log Stationary Fractional Brownian Motion(LogS-fBM)model, introduced by Peng, Bacry, and Muzy , describes a log-volatility process driven by a stationary fractional Brownian motion (S-fBM). This model is characterized by three key parameters: the intermittency parameter λ, the correlation scale T, and the Hurst exponent H. Notably, as H approaches zero, the model’s multifractal random measure (volatility measure) converges to that of the multifractal random walk introduced by Bacry et al.. In contrast, when H ≈0.1, the model captures rough volatility dynamics. A multidimensional extension of the Log S-fBM model, referred to as the m-Log S-fBM was also developed. In this framework, the log-volatilities of multiple assets are correlated, with dependencies governed by both the cointermittency matrix and the coHurst matrix. These matrices ensure that the marginal distributions of the model retain the one-dimensional Log S-fBM dynamic. A key analytical tool for studying this model is the small intermittency approximation, which allows to approximate the generalized moments of the normalized log-volatility over a time period ∆ > 0 using the moments of the integrated S-fBM process over the same period when λ^2 is small. This approximation is particularly relevant given the empirical findings of Wu et al., who observed that for various assets, λ^2 ≈0.02. Besides, the Log S-fBM model can be used in the Nested factor model, introduced by Bouchaud et al., where the asset return fluctuations are explained by common factors representing the market economic sectors and residuals (noises). These residuals share with the factors a common dominant volatility mode in addition to the idiosyncratic mode unique to each residual. Here, we consider the case of a single factor, where the only dominant common mode is a S-fBM process with Hurst exponent H ≃0.11, while the residuals, in addition to the previous common mode, contain idiosyncratic components with Hurst exponents H ≃0. Furthermore, we propose a statistical procedure to estimate the Hurst factor exponent from stock return dynamics, providing theoretical guarantees. The method performs well in the limit where the number of stocks N tends to infinity. In this talk, we introduce the Log S-fBM model in its one-dimensional and multidimensional forms, present the calibration procedure based on the small intermittency approximation, and discuss the Nested Log S-fBM factor model.
Salle : A707
Colloque
Colloquium du CEREMADE
WANG Yilin (IHES)
Le 04/03/2025
De 15:30 à 16:30
Titre : The Brownian loop measure on Riemann surfaces and applications to length spectra
Résumé : The goal of this talk is to showcase how we can use stochastic processes to study the geometry of surfaces. More precisely, we use the Brownian loop measure to express the lengths of closed geodesics on a hyperbolic surface and zeta-regularized determinant of the Laplace-Beltrami operator. This gives a tool to study the length spectra of a hyperbolic surface and we obtain a new identity between the length spectrum of a compact surface and that of the same surface with an arbitrary number of additional cusps. This is based on a joint work with Yuhao Xue (IHES).
Salle : A709
Séminaire
Séminaire des jeunes chercheurs
SURIN Alexandre (CEREMADE)
Le 06/03/2025
De 17:00 à 18:00
Titre : Long time behavior of a non linear Fokker-Planck equation with multiple steady states
Résumé : We consider a Fokker-Planck equation which is the mean-field limit of an interacting particles system with a temperature parameter $D>0$, a confinement potential $V$ and an interacting kernel $K$. The solution to this equation can be seen as the gradient flow of the "free energy" in the space of probability measure with Wasserstein 2 distance. Taking a specific potential of "self-propulsion" and an interacting kernel which tends to align the velocity of a particle with the average velocity, we observe a phase transition that is a limit temperature $D_*$ under which there is a continuum of steady states. We will answer the two following question: -Do the free energy of the solution converges to the free energy of a steady state ? -If the answer to the precedent question is yes, do the solution converges to a specific steady state ?
Salle : A707
Séminaire
Séminaire Analyse-Probabilités
JEGO Antoine (CNRS - Université Paris Dauphine)
Le 11/03/2025
De 10:30 à 11:30
Titre : Integration by parts in random conformal geometry
Résumé : Random objects satisfying a conformal invariance property naturally appear from the scaling limit of critical models of statistical mechanics. Examples include Schramm—Loewner Evolutions (SLE), the Gaussian free field (GFF), or even more classically, planar Brownian motion. In this talk, I will present our new approach to random conformal geometry based on the derivation of integration by parts formulas. I will in particular focus on two applications: our proof of the Kontsevich—Suhov conjecture and our new approach to random conformal weldings (Sheffield’s celebrated quantum zipper). Based on joint works with Guillaume Baverez.
Salle : Amphi 1
Séminaire
Séminaire des jeunes chercheurs
LE GALL Théophile (CEREMADE)
Le 13/03/2025
De 17:00 à 18:00
Titre : A particle method for McKean-Vlasov equation with common noise
Résumé : The McKean-Vlasov equation with common noise can be discretized in two steps: first in time using the Euler scheme, and then in space through a particle method, leveraging the propagation of chaos property. Under suitable regularity assumptions—Hölder continuity in time and Lipschitz continuity in both the state and measure arguments—convergence rates are established for both the Euler scheme and the particle method. These results extend previous analyses to the setting with common noise. Finally, the effectiveness of the approach can be illustrated through two simulation examples: a modified conditional Ornstein-Uhlenbeck process with common noise and an interbank market model.
Salle : A707
Séminaire
Séminaire Analyse-Probabilités
LACKER Daniel (Columbia University)
Le 18/03/2025
De 10:30 à 11:30
Titre : Projected Langevin dynamics and a gradient flow for entropic optimal transport
Résumé : The classical Langevin diffusion provides a natural algorithm for sampling from its invariant measure, which can be characterized as the unique minimizer of an energy functional over the space of probability measures. We introduce an analogous diffusion process that samples from an entropy-regularized optimal transport (a.k.a. Schrodinger bridge), which uniquely minimizes the same energy functional but constrained to the set of couplings of two given marginal probability measures. The law of the diffusion remains a coupling at each time if initialized as such. In addition, we show an exponential convergence rate by means of a new kind of logarithmic Sobolev inequality, in the case of sufficiently high temperature and (asymptotically) log-concave marginals. The dynamics can be viewed as a gradient flow on the space of couplings, viewed as a submanifold of Wasserstein space. Analogous constructions are possible for other constrained sampling problems, and as time permits I will discuss the surprisingly closely related example of mean field variational inference in Bayesian statistics.
Salle : A711
Séminaire
Rencontres statistiques
DUCHEMIN Quentin (EPFL)
Le 24/03/2025
De 13:30 à 14:30
Titre : Pinball Quantile Regression Trees for Conformal Prediction
Résumé : Conformal prediction, known for providing model-agnostic uncertainty quantification, has become an essential tool with a mushrooming number of applications. An ideal conformal prediction method should be adaptive, data-efficient, and interpretable. To meet these criteria, we propose to improve existing quantile-based conformal methods using Pinball quantile regression trees. Moreover, we introduce a new quantile out-of-bag framework that is shown empirically to provide smaller conformal prediction sets while maintaining rigorous theoretical guarantees for coverage. Page web : http://quentin-duchemin.alwaysdata.net/wiki/
Salle : P428
Séminaire
Séminaire Analyse-Probabilités
ARCHER Eleanor (Ceremade - Université Paris Dauphine PSL)
Le 25/03/2025
De 10:30 à 11:30
Titre : Scaling limits of random spanning trees
Résumé : A spanning tree of a finite connected graph G is a connected subgraph of G that contains every vertex and contains no cycles. A well-known result of Aldous states that the scaling limit of a uniformly chosen spanning tree of the complete graph is the Brownian tree (CRT). In fact, this statement is more general: the Brownian tree is the scaling limit of uniform spanning trees for a large set of high-dimensional graphs. In this talk, we'll try to explain this universal phenomenon. Time permitting, we will also discuss the scaling limits of non-uniform random spanning trees. Based on joint works with Asaf Nachmias and Matan Shalev.
Salle : A709
Séminaire
Séminaire des jeunes chercheurs
MASSOULIÉ Brune (CEREMADE)
Le 27/03/2025
De 17:00 à 18:00
Titre : Cutoff for the mixing time of the facilitated exclusion process
Résumé : The facilitated exclusion process (FEP) is a particle system, where particles evolve on a discrete lattice, making random jumps while obeying local constraints. Its evolution rules mean that some zones are frozen while others have movement, thus modelling a liquid-solid interface. After a transience time, it is either completely frozen or reaches an ergodic component. We estimated this transience time, using a mapping to another process, the SSEP with traps. When the FEP doesn’t freeze and continues moving, one can study its mixing time, meaning the time needed to be close to equilibrium. The cutoff phenomenon is the very abrupt decrease of the distance to equilibrium with time, and has been observed in many Markov chains, the historical example being card shufflings. We prove cutoff for the mixing time of the FEP, by showing the time spent in the transient phase and the ergodic phase balance each other out.
Salle : A707
Séminaire
Rencontres statistiques
OCELLO Antonio (Polytechnique)
Le 31/03/2025
De 13:30 à 14:30
Titre : Theoretical Advances in Score-Based Generative Models: Convergence Bounds and Noise Schedule Optimization
Résumé : Score-based generative models (SGMs) have emerged as a state-of-the-art framework for sampling from complex data distributions, leveraging the estimation of score functions through noise-perturbed samples. A central challenge in understanding SGMs lies in quantifying their convergence to the target distribution. Various works have analyzed this convergence using Kullback-Leibler (KL) divergence and Wasserstein distances, often under restrictive assumptions.In this talk, I will present an overview of existing convergence bounds for SGMs and introduce two recent contributions that provide a refined theoretical understanding of their performance. First, I will discuss our work on the impact of the noise schedule on generative performance, where we establish explicit upper bounds for the KL divergence and Wasserstein-2 distance under mild assumptions. This result not only improves upon prior state-of-the-art bounds but also provides practical insights into hyperparameter selection. Building on this framework, I will then present recent advances in Wasserstein-2 convergence analysis. By leveraging the regularization properties of the Ornstein–Uhlenbeck (OU) process, we relax the traditional assumptions of log-concavity and score regularity. Our approach reveals that weakly log-concave distributions evolve towards log-concavity, and we establish a novel characterization of the dynamics of score function contraction and non-contraction. This enables more general and widely applicable convergence results, particularly for complex distributions such as Gaussian mixtures. This talk is based on joint work with Stanislas Strasman, Claire Boyer, Sylvain Le Corff, and Vincent Lemaire, recently accepted to Transactions on Machine Learning Research (https://openreview.net/forum?id=BlYIPa0Fx1), as well as a recent preprint in collaboration with Marta Gentiloni-Silveri (https://arxiv.org/abs/2501.02298).
Salle : A711
Colloque
Colloquium du CEREMADE
REYNAUD-BOURET Patricia (Université Côte d'Azur)
Le 01/04/2025
De 15:30 à 16:30
Titre : Kalikow decomposition for the study of neuronal networks: simulation and learning
Résumé : Kalikow decomposition is a decomposition of stochastic processes (usually finite state discrete time processes but also more recently point processes) that consists in picking at random a finite neighborhood in the past and then make a transition in a Markov manner. This kind of approach has been used for many years to prove existence of some processes, especially their stationary distribution. In particular, it allows to prove the existence of processes that model infinite neuronal networks, such as Hawkes like processes or Galvès-Löcherbach processes. But beyond mere existence, this decomposition is a wonderful tool to simulate such network, as an open physical system, that from a computational point of view could be competitive with the most performant brain simulations. This decomposition is also a source of inspiration to understand how local rules at each neuron can make the whole network learn.
Salle : A709
Séminaire
Séminaire des jeunes chercheurs
LEBLANC Théo (CEREMADE)
Le 03/04/2025
De 17:00 à 18:00
Titre : Hawkes and Autoregressive processes in Neuroscience
Résumé : In this talk we present a special class of point processes: Hawkes processes and focus on how Hawkes processes can be used in Mathematical Neuroscience to model functional connectivity. In neuroscience, functional connectivity can be seen as an ensemble of interactions between brain oscillations (rhythms) and individual neuronal activity (spikes). Neuronal activity can be modeled by a multivariate Hawkes process. The points of the Hawkes process correspond to the spiking times of each neurons and the spiking activity at time t depends on past spikes of the different neurons. Brain rhythms, another important quantity about brain activity, can be defined as the wavelet coefficients of the LFP (local field potential) signals and are therefore treated as discrete sequences. Autoregressive equations are the standard way of modeling interactions between brain rhythms. We introduce a coupled model combining both Hawkes and AutoRegressive processes to describe at once all possible interactions between neurons and brain rhythms. We present theoretical results and a statistical method based on the LASSO to infer functional connectivity.
Salle : A707
Séminaire
Rencontres statistiques
GUEDON Tom (INRAE)
Le 07/04/2025
De 16:00 à 17:00
Titre : Estimation de ratio de constante de normalisation: l'algorithme SARIS.
Résumé : Le calcul des rapports de constante de normalisation joue un rôle important dans la modélisation statistique. Deux exemples notables sont les tests d’hypothèses dans les modèles à variables latentes et la comparaison de modèles en statistique bayésienne. Dans ces deux cas, le rapport de vraisemblance et le facteur de Bayes sont définis comme le rapport des constantes de normalisation des distributions a posteriori. Nous proposons dans cet article une nouvelle méthodologie qui estime ce rapport en utilisant le principe de l’approximation stochastique. Notre estimateur est consistant et asymptotiquement gaussien. Sa variance asymptotique est plus faible que celle de l’estimateur populaire bridge sampling. En outre, il est beaucoup plus robuste lorsque les supports des deux distributions non normalisées considérées se chevauchent peu. Grâce à sa définition en ligne, notre procédure peut être intégrée dans un processus d'estimation dans les modèles à variables latentes, ce qui permet ainsi de réduire l’effort de calcul. Les performances de l’estimateur sont illustrées par une étude de simulation et comparées à celles de deux autres estimateurs : le ratio importance sampling et le bridge sampling.
Salle : B315
Séminaire
Séminaire des jeunes chercheurs
SOENEN Guillaume (CEREMADE)
Le 10/04/2025
De 17:00 à 18:00
Titre : Hydrodynamic limit of a particle system
Résumé : In this talk, we consider a particle system where particles evolve along a line at constant speed. This system has already been studied with some boundary conditions (particles on a torus or confined between two walls), but we propose here an unsolved problem, where the particles are evolving between a wall on one side and some pressure force on the other side. As this system is not easy to understand, we add a thermalization phenomenon, ie some probabilistic term in the equation (here it will be Langevin dynamics). The goal is to compute the hydrodynamic limit of this system : the idea is to describe the macroscopic behavior from the microscopic equations. It will lead us to study a free boundary partial differential equation and the uniqueness of its weak solutions.
Salle : A707
Séminaire
Séminaire Analyse-Probabilités
DOLBEAULT Jean (CNRS CEREMADE)
Le 29/04/2025
De 10:30 à 11:30
Titre : Résultats de stabilité pour des inégalités fonctionnelles : flots paraboliques non-linéaires et méthodes d'entropie
Résumé : Il est possible d'obtenir des estimations explicites de stabilité grâce à des flots paraboliques non-linéaires, des méthodes d'entropie et des estimations spectrales directes, éventuellement combinées à des méthodes du calcul des variations. Ces méthodes s'appliquent aux inégalités de Sobolev, de Gagliardo-Nirenberg ou de Sobolev logarithmique sur la sphère ou sur l'espace Euclidien (avec mesure de Lebesgue ou mesure Gaussienne). L'exposé sera consacré à une revue de résultats récents obtenus en particulier avec M. Bonforte, G. Brigati, B. Nazaret et N. Simonov.
Salle : A711
Colloque
Colloquium du CEREMADE
FRANK Rupert (Ludwig Maximilians Universität München)
Le 06/05/2025
De 15:30 à 16:30
Titre : Sharp functional inequalities and their stability
Résumé : The Sobolev inequality is a paradigmatic example of a functional inequality with many applications in the Calculus of Variations, Geometric Analysis and PDEs. In some of these applications the optimal value of the constant is of importance, as is a characterization of the set of optimizers. The stability question is whether functions whose Sobolev quotient is almost minimal are close to minimizers of the inequality and, if so, in which sense. We give a gentle introduction to this question and review some recent results on the Sobolev inequality and other functional inequalities of a similar nature.
Salle : A709
Séminaire
Séminaire Analyse-Probabilités
DEMBIN Barbara (Université de Strasbourg)
Le 13/05/2025
De 10:30 à 11:30
Titre : Surfaces minimales en environnement aléatoire
Résumé : Nous considérons des surfaces de Z^d dans R et un environnement aléatoire eta dans Z^d x R. Nous nous intéressons aux surfaces varphi qui minimisent la somme de leur énergie élastique (norme l_2 dans Z^d du gradient de la surface) et du bruit sur la surface sum_v eta_{v,varphi_v}. Lorsque le bruit est un brownien fractionnaire, nous obtenons la valeur des exposants liés aux fluctuations en énergie et en espace. Travail en commun avec Dor Elboim et Ron Peled
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
DONADINI Anna (Università degli Studi di Milano Bicocca)
Le 20/05/2025
De 17:00 à 18:00
Titre : Noise sensitivity: Boolean setting and beyond
Résumé : The study of boolean functions arises naturally in the context of computer science and combinatorics. However, over the last 30 years, it was recognized that some of the properties which hold for boolean functions have deep implications in statistical physics. In this talk, we will particularly focus on noise sensitivity, first introduced in 1998 by Benjamini, Kalai and Schramm, by analyzing the most fundamental concepts of the theory and presenting some extensions of the main classical results.
Salle : A707
Séminaire
Séminaire Analyse-Probabilités
GLOGIC Irfan (Bielefeld University)
Le 20/05/2025
De 10:30 à 11:30
Titre : On self-similar blowup for supercritical dispersive PDEs
Résumé : Numerical simulations of different types of supercritical evolution equations show certain degree of universality when it comes to formation of singularities. Specifically, it appears that the generic blowup behavior and threshold for blowup phenomena are both governed by self-similar solutions. In this talk, we explore these observations in the context of the focusing cubic wave equation in the energy-supercritical regime, d≥5. We begin by reviewing the results leading to a complete proof of the non-radial stability of the so-called ODE blowup profile. Next, we present what appears to be the only nontrivial self-similar solution known in closed form. We then show numerical evidence suggesting that this solution acts as a generic attractor within the threshold for the ODE blowup. Finally, as the first step toward rigorously showing this observation, we outline our proof of the non-radial co-dimension one stability of this solution. At the end we will comment on the analogous results/conjectures for other supercritical dispersive models. The talk is based on joint works with Maciej Maliborski (Vienna) and Birgit Schörkhuber (Innsbruck).
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
DAVRON Lucas (CEREMADE)
Le 22/05/2025
De 17:00 à 18:00
Titre : A criterion for exact output tracking, for some SISO systems
Résumé : In control theory we often consider equations of the form $x'(t) = Ax(t) + Bu(t)$ and try to choose the command $u(t)$ so as $x(t)$ reaches some target, e.g. $x(T) = x_T$ for some given $x_T$ and fixed time $T$. In some cases it is actually better suited to achieve another control objective: the output tracking. For this we define an output signal $y(t) = Cx(t) + Du(t)$ and we aim at selecting $u(t)$ so as $y(t)$ matches some reference signal, e.g. $y(t) = y_{ref}(t)$ for all times $t$. With this in mind, one of the most basic question one may ask is: what are these output signals $y$ that the system may generate? Surprisingly there is no satisfactory answer in the literature, even in the basic case where the system has a single input and a single output (SISO), meaning that both $u(t)$ and $y(t)$ are numbers. In finite dimension the situation is fully understood thanks to the theory of Volterra integral equations. In infinite dimension the latter does not help anymore and we rely on a new result for exterior multipliers on Hardy spaces, providing a partial answer to the previous question.
Salle : A707
Séminaire
Rencontres statistiques
THOMAS Arthur (LEDA)
Le 26/05/2025
De 15:30 à 16:30
Titre : Forecasting extreme trajectories using seminorm representations
Résumé : For (Xt) a two-sided α-stable moving average, this paper studies the conditional distribution of future paths given a piece of observed trajectory when the process is far from its central values. Under this framework, vectors of the form Xt = (Xt−m, . . . ,Xt,Xt+1, . . . ,Xt+h), m ≥ 0, h ≥ 1, are multivariate α-stable and the dependence between the past and future components is encoded in their spectral measures. A new representation of stable random vectors on unit cylinders sets {s ∈ Rm+h+1 : ∥s∥ = 1} for ∥ °§ ∥ an adequate seminorm is proposed to describe the tail behaviour of vectors Xt when only the first m + 1 components are assumed to be observed and large in norm. Not all stable vectors admit such a representation and (Xt) will have to be “anticipative enough” for Xt to admit one. The conditional distribution of future paths can then be explicitly derived using the regularly varying tails property of stable vectors and has a natural interpretation in terms of pattern identification. Through Monte Carlo simulations we develop procedures to forecast crash probabilities and crash dates and demonstrate their finite sample performances. As an empirical illustration, we estimate probabilities and reversal dates of El Nino and La Nina occurrences.
Salle : A711
Séminaire
Séminaire Analyse-Probabilités
SCHAPIRA Barbara (Université de Montpellier)
Le 27/05/2025
De 10:30 à 11:30
Titre : Entropies à l'infini et applications
Résumé : Je vais donner plusieurs définitions d'entropie à l'infini pour un système dynamique sur un espace topologique non compact. Je vais (peut-être) montrer qu'elles coincident. Lorsque l'entropie à l'infini est strictement inférieure à l'entropie topologique, dans le cas du flot géodésique en courbure négative, nous obtenons de nombreuses applications intéressantes. travail en commun avec S. Gouezel et S. Tapie.
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
MALAMUT Hugo (CEREMADE)
Le 12/06/2025
De 17:00 à 18:00
Titre : Well-posedness and convergence of entropic approximation of semi-geostrophic equations
Résumé : The semi-geostrophic (SG) equations are essential for modeling the evolution of large-scale wind fronts. Optimal transport theory offers a compact interpretation of these equations and some notion of week solution. In the first part of this talk, I will present the connections that arise between optimal transport and fluid dynamics, following Yann Brenier’s interpretation of both Arnold’s work on the Euler equations from the 1960s and the formulation of the SG equations by Hoskins, Cullen, and their coauthors in the 1970s-1980s. Building on this foundation, I will then discuss how the entropic approximation method provides a practical numerical resolution of the SG equations through the Sinkhorn algorithm. This approach corresponds to a PDE approximation of the SG system. I will present well-posedness results for this PDE and analyze the convergence of the entropic scheme as both the regularization parameter and the discretization step vanish. This presentation is based on joint works with J.-D. Benamou and C. Cotter (JCP, 2023) as well as G. Carlier (arxiv, 2024)
Salle : A707
Séminaire
Séminaire des jeunes chercheurs
MALAMUT Hugo (CEREMADE)
Le 12/06/2025
De 17:00 à 18:00
Titre : Well-posedness and convergence of entropic approximation of semi-geostrophic equations
Résumé : The semi-geostrophic (SG) equations are essential for modeling the evolution of large-scale wind fronts. Optimal transport theory offers a compact interpretation of these equations and some notion of week solution. In the first part of this talk, I will present the connections that arise between optimal transport and fluid dynamics, following Yann Brenier’s interpretation of both Arnold’s work on the Euler equations from the 1960s and the formulation of the SG equations by Hoskins, Cullen, and their coauthors in the 1970s-1980s. Building on this foundation, I will then discuss how the entropic approximation method provides a practical numerical resolution of the SG equations through the Sinkhorn algorithm. This approach corresponds to a PDE approximation of the SG system. I will present well-posedness results for this PDE and analyze the convergence of the entropic scheme as both the regularization parameter and the discretization step vanish. This presentation is based on joint works with J.-D. Benamou and C. Cotter (JCP, 2023) as well as G. Carlier (arxiv, 2024)
Salle : A707
Séminaire
Séminaire Analyse-Probabilités
NGUYEN Van Tien (National Taiwan University)
Le 08/07/2025
De 15:30 à 16:30
Titre : Blowup solutions to the Keller-Segel system
Résumé : I will present the construction of various blowup solutions to the Keller-Segel system, including exact self-similar solutions, those exhibiting asymptotically self-similar profiles, and the formation of single-collapsing blowup. Furthermore, the talk will cover more complex patterns such as multiple-collapsing, standing-ring and collapsing-ring blowup, showcasing the rich phenomenology achievable through these rigorous constructions.
Salle : A707
Séminaire
Rencontres statistiques
KILLICK Rebecca (Lancaster University)
Le 08/09/2025
De 13:45 à 14:45
Titre : Adaptive shrinkage for autocorrelation
Résumé : It has long been known that the sample autocorrelation (ACF) and partial autocorrelation (PACF) functions underestimate the magnitude of correlation in stationary time series. Although finite bias correction formulae can be found their use typically increases estimator variability. On the other hand, shrinking estimators toward zero can reduce variance but increase bias resulting in higher mean squared error for some correlation structures. This paper introduces a novel, computationally efficient, penalised M-estimator for (partial) autocorrelation, with the penalty pushing the estimator toward a target selected from the data. This both encapsulates and differs from previous attempts at penalised estimation for autocorrelation, which shrink the estimator toward the target value of zero. We provide data-driven target and tuning parameters which improve estimation of the ACF and PACF in finite samples and the limit. The estimators of the PACF can be used to efficiently fit autoregressive models, with the resulting estimators satisfying an oracle property. Additionally, we introduce an AIC statistic using the penalised PACF, which provides consistent estimation of the true order within the autoregressive class, a result sorely amiss from this literature to date.
Salle : F307
Séminaire
Séminaire des jeunes chercheurs
BRIGATI Giovanni (ISTA)
Le 11/09/2025
De 17:00 à 18:00
Titre : Nonlinear diffusion flows and constructive stability for interpolation and logarithmic Sobolev inequalities
Résumé : We analyse three different stability problems for functional inequalities. We investigate Gagliardo—Nirenberg inequalities on the sphere, and Beckner’s inequalities in the Gaussian space, as a rigorous infinite-dimensional limit of those. Finally, as the critical endpoint of Beckner’s inequalities, we consider the Gaussian LSI. Stability results are provided, in a constructive fashion, via a flow-based technique, combined with spectral analysis, and precise Taylor expansions. The presentation is based on a series of papers by Jean Dolbeault, Nikita Simonov, and the speaker.
Salle : A411
Séminaire
Séminaire Analyse-Probabilités
GERMAIN Pierre (Imperial College London)
Le 16/09/2025
De 10:30 à 11:30
Titre : Asymptotic stability of solitary waves in dimension one
Résumé : I will present work on the asymptotic stability of solitary waves for two 1D models: nonlinear Klein-Gordon (kinks), and nonlinear Schrodinger (bright solitons). An important idea in the proof is the treatment of resonances through the distorted Fourier transform. This is joint work with Fabio Pusateri and Charles Collot.
Salle : A709
Séminaire
Séminaire Analyse-Probabilités
LETROUIT Cyril (LMO Paris Orsay)
Le 23/09/2025
De 10:30 à 11:30
Titre : Quantitative stability in optimal transport
Résumé : Optimal transport consists in sending a given source probability measure \rho to a given target probability measure \mu in an optimal way with respect to a certain cost. On bounded subsets of R^d, if the cost is given by the squared Euclidean distance and if \rho is absolutely continuous, there exists a unique optimal transport map from \rho to \mu. Optimal transport has been widely applied across various domains, notably in analysis, probability, statistics, geometry and optimization. In this talk, we provide a quantitative answer to the following stability question: if \mu is perturbed, can the optimal transport map from \rho to \mu change significantly? The answer depends on the properties of the density \rho. This question takes its roots in numerical optimal transport, and has found applications to other problems like the statistical estimation of optimal transport maps, the computation of Wasserstein barycenters, and the convergence of Sinkhorn's algorithm. The talk is based on joint works with Quentin Mérigot and Jun Kitagawa.
Salle : A711
Séminaire
Rencontres statistiques
FERMANIAN Jean-Baptiste (Université de Montpellier)
Le 29/09/2025
De 12:00 à 13:00
Titre : Class conditionnal conformal prediction for multiple inputs by p-value aggregation
Résumé : Conformal prediction methods are statistical tools designed to quantify uncertainty and generate predictive sets with guaranteed coverage probabilities. The work I will present, introduces a refinement to these methods for classification tasks, specifically tailored for scenarios where multiple observations (multi-inputs) of a single instance are available at prediction time. Our approach is particularly motivated by applications in citizen science, where multiple images of the same plant or animal are captured by individuals. Our method integrates the information from each observation into conformal prediction, enabling a reduction in the size of the predicted label set while preserving the required class-conditional coverage guarantee. The approach is based on the aggregation of conformal p-values computed from each observation of a multi-input. By exploiting the exact distribution of these p-values, we propose a general aggregation framework using an abstract scoring function, encompassing many classical statistical tools. Knowledge of this distribution also enables refined versions of standard strategies, such as majority voting. The method is evaluated on simulated and real data, with a particular focus on Pl@ntNet, a citizen science platform that facilitates the collection and identification of plant species through user-submitted images. This work has been done in collaboration with Joseph Salmon (Université de Montpellier, Inria) and Mohamed Hebiri (Université Gustave Eiffel).
Salle : F203
Séminaire
Séminaire Analyse-Probabilités
CONTAT Alice (Université Sorbonne Paris Nord)
Le 30/09/2025
De 10:30 à 11:30
Titre : Brûler la grille et équation de Blasius
Résumé : On se place sur le tore (discret) de côté n et de dimension d. Imaginons qu’un pyromane allume des départ de feu alors que pendant ce temps, le feu se propage le long des arêtes. Au bout de combien de temps le tore sera entièrement brûlé ? De manière peut-être surprenante, la réponse à cette question est liée à l’étude de l’équation de Blasius y^(d+1) = y \cdot y^(d). Basé sur des travaux en commun avec Guillaume Blanc.
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
DETZEN Louis (CEREMADE)
Le 02/10/2025
De 17:00 à 18:00
Titre : Phase transitions for infinite systems of bosons and fermions
Résumé : The rigorous modelling of infinite systems, whether classical or quantum, is a very difficult problem that has occupied researchers since the 1960s. A very famous problem, essentially still completely open at the present time, concerns the existence and nature of phase transitions, particularly fluid-solid transitions. For instance, we are currently unable to prove that water becomes solid at 0 °C (under normal pressure conditions)! Most existing results pertain to discrete systems (on a lattice). We will explore some recent results about the existence of phase transitions for a infinite system of bosons particles, which come from an article written by Mathieu Lewin (CEREMADE, CNRS) and Phan Thành Nam (LMU Munich), as well as a few results with fermions that I worked on. I will show some numerical results in 1D as well.
Salle : A707
Colloque
Colloquium du CEREMADE
DESOLNEUX Agnès (ENS Paris-Saclay)
Le 07/10/2025
De 15:30 à 16:30
Titre : Mathematical Models for Texture Image Synthesis
Résumé : In this talk, I will present several mathematical models for the problem of texture image synthesis. This problem consists in generating new images from a single exemplar image. Two main classes of models will be considered. The first one is the “copy-and-paste” type, and can be formalized using Markov chains. The second one is of a statistical nature: it consists in computing a set of statistics on the exemplar image and then generating new images that have these statistics. I will focus in particular on this latter approach, emphasizing models based on constrained maximum entropy distributions.
Salle : A709
Séminaire
Séminaire Analyse-Probabilités
HAMZA Mohammed Ali (Imam Abdulrahman Bin Faisal University)
Le 09/10/2025
De 10:30 à 11:30
Titre : The blow-up rate for some nonlinear evolution equations without scale invariance
Résumé : In this talk, we discuss some evolution equations with logarithmic nonlinearity in the subconformal case. We show that all blow-up solutions in the subconformal range are Type I solutions. This will constitute a good start in proving that the scale invariance property is not crucial in deriving the blow-up rate.
Salle : A711
Séminaire
Séminaire Outils informatiques
INDJIC Marko (CEREMADE)
CHUPIN Maxime
Le 09/10/2025
De 14:00 à 15:30
Titre : Présentation du cluster
Résumé :
Salle : A701
Séminaire
Séminaire Analyse-Probabilités
KRUPA Sam (ENS Paris)
Le 14/10/2025
De 10:30 à 11:30
Titre : Are $L^\infty$ solutions to hyperbolic systems of conservation laws unique?
Résumé : For hyperbolic systems of conservation laws in 1-D, fundamental questions about uniqueness and blow up of weak solutions still remain even for the apparently “simple” systems of two conserved quantities such as isentropic Euler and the p-system. Similarly, in the multi-dimensional case, a longstanding open question has been the uniqueness of weak solutions with initial data corresponding to the compressible vortex sheet. We address all of these questions by using the lens of convex integration, a general method of constructing highly irregular and non-unique solutions to PDEs. Our proofs involve computer-assistance. This talk is based on joint work with László Székelyhidi, Jr.
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
NDIAYE Aminata (CEREMADE)
Le 16/10/2025
De 17:00 à 18:00
Titre : Marginal contrastive discrimination for conditional density estimation
Résumé : Conditional density estimation is a central problem in statistics and machine learning, particularly when the target variable Y is univariate but the conditioning set X is high dimensional. Traditional methods often struggle in this regime due to the curse of dimensionality. We propose Marginal Contrastive Discrimination (MCD ), a novel approach that reformulates conditional density estimation as a combination of marginal density estimation and binary classification. The key idea is to construct a contrastive training dataset by mixing true pairs (X, Y) with independent samples, allowing for controlled joint–marginal mixtures. This framework naturally extends to settings with additional marginal data or multiple targets per observation, enabling principled dataset enlargement while preserving theoretical guarantees. Experiments demonstrate that MCD achieves performance comparable to, and sometimes exceeding, state-of-the-art conditional density estimators, particularly in high-dimensional conditioning spaces.
Salle : A707
Séminaire
Rencontres statistiques
GRUFFAZ Samuel (ENS Paris-Saclay)
Le 20/10/2025
De 13:45 à 14:45
Titre : Demystifying Markov Chain Monte Carlo (MCMC): Convergence Theory and Practical Tuning
Résumé : Markov Chain Monte Carlo (MCMC) methods are used to approximately sample from a target probability distribution, which is useful in Bayesian computation and, more generally, in numerical approximation. In theory, we must ensure that the Markov chain underlying an MCMC method converges to the target distribution. In practice, the goal is to tune the hyperparameters to achieve fast convergence and make the MCMC algorithm efficient. In this presentation, I will demystify these topics and highlight the link between theory and applications through the lens of my own research.
Salle : P303
Séminaire
GTD Systèmes Dynamiques
FEJOZ Jacques (Université Paris Dauphine)
Le 03/11/2025
De 10:00 à 11:00
Titre : Introduction à la dynamique de N vortex
Résumé : Les systèmes de vortex dans un domaine du plan forment une sorte de sous-problème invariant de dimension finie des équations d'Euler pour les fluides parfaits incompressibles. Tout comme les équations d'Euler elles-mêmes en dimension infinie, ils sont un système hamiltonien, avec un riche espace de paramètres contenant notamment la géométrie du domaine. Nous montrerons quelques directions d'étude de ce riche sujet, qui diffère fondamentalement du problème des N corps en mécanique céleste. L'exposé sera un mélange de remarques classiques et d'un travail en cours avec Mar Giralt, Éric Séré et Wang Qun, dans le cas de deux vortex, sur l'existence de solutions périodiques et quasi-périodiques et la non-intégrabilité.
Salle : A413
Colloque
Colloquium du CEREMADE
BARRAQUAND Guillaume (ENS Paris)
Le 04/11/2025
De 15:30 à 16:30
Titre : Extreme diffusion
Résumé : Diffusion phenomena are ubiquitous in nature and have been studied theoretically for more than a century. Still, the influence of a random environment on diffusion is not very well understood. I will discuss about the simplest possible model of diffusion in random environment: a simple random walk. We will see that using methods coming from integrable systems, one can relate the extreme statistics of diffusive particles in random environment to an area of Statistical Physics called the Kardar-Parisi-Zhang universality class.
Salle : A709
Séminaire
Séminaire des jeunes chercheurs
OUYANG Zikun (CEREMADE)
Le 06/11/2025
De 17:00 à 18:00
Titre : Integrable directed polymers and their stationary measures
Résumé : Directed polymers are an important family of models in the Kardar–Parisi–Zhang (KPZ) universality class, providing a probabilistic framework for studying random interface growth and disordered systems. However, exact statistical results are available only for models with specially chosen disorders, known as the integrable ones. This talk will present several integrable directed polymer models in different space–time geometries, with a focus on their stationary measures. We will explain how these stationary structures can be used to deduce laws of large numbers for the corresponding free energies. Time permitting, we will also discuss recent developments on polymer models with matrix-valued disorder, based on joint work with Guillaume Barraquand.
Salle : A707
Séminaire
Séminaire des jeunes chercheurs
TABARY Côme (Université Paris-Cité)
Le 13/11/2025
De 17:00 à 18:00
Titre : An introduction to propagation of chaos illustrated by the Boltzmann and Landau equations
Résumé : The Boltzmann equation provides a statistical description of dilute gas at a mesoscopic scale, intermediate to microscopic particle interactions and macroscopic fluid mechanics. A deep ansatz in its derivation is the assumption of molecular chaos, that has puzzled mathematicians and physicists for decades: It claims that any two gas particles are uncorrelated before interacting with each other, disregarding the previous interactions that should have made them correlated. In 1956, Mark Kac proposed to justify this ansatz by starting from a simpler Markov process of N particles, and letting N go to infinity. He claimed that the law of the N particles should approach the N-fold tensor product of the solution of the Boltzmann equation, a limit now known as propagation of chaos: this would indeed show that the particles become independent of each other in the large N limit, despite constantly interacting with each other. In this talk, I will introduce the Boltzmann equation as well as its close cousin the Landau equation, which is used to model plasmas, and showcase their key properties. I will motivate Kac's program for these equations, highlight the mathematical challenges it poses, and present a proof of the propagation of chaos for the Landau equation.
Salle : A707
Séminaire
GTD Systèmes Dynamiques
FEJOZ Jacques (Université Paris Dauphine)
Le 17/11/2025
De 10:00 à 11:00
Titre : Introduction à la dynamique de N vortex
Résumé :
Salle : C131
Séminaire
Séminaire Analyse-Probabilités
CERCLÉ Baptiste (EPFL Lausanne)
Le 18/11/2025
De 10:30 à 11:30
Titre : Around the semi-classical limit of boundary Liouville theory
Résumé : Liouville theory provides a notion of random surface that "fluctuates" around a deterministic (=classical) one. This classical geometry corresponds to the unique solution of the problem of finding, within a given conformal class, a Riemannian metric with prescribed scalar and geodesic curvatures as well as conical singularities and corners. The level of randomness in Liouville theory is measured by the coupling constant $\gamma\in(0,2)$, the semi-classical limit corresponding to taking $\gamma\to0$. In this talk we will first discuss this classical geometry and the analytic tools used to study it. In a second part we will explain, thanks to its probabilistic formulation based on Gaussian Free Fields and Gaussian Multiplicative Chaos, that the semi-classical limit of boundary Liouville CFT indeed describes this classical geometry. If time permits we will discuss some implications of this semi-classical limit in relation with uniformisation of open Riemann surfaces.
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
LUCIANO Antoine (CEREMADE)
Le 20/11/2025
De 17:00 à 18:00
Titre : Permutations accelerate Approximate Bayesian Computation
Résumé : Approximate Bayesian Computation (ABC) methods have become essential tools for performing inference when likelihood functions are intractable or computationally prohibitive. However, their scalability remains a major challenge in hierarchical or high-dimensional models. In this paper, we introduce permABC, a new ABC framework designed for settings with both global and local parameters, where observations are grouped into exchangeable compartments. Building upon the Sequential Monte Carlo ABC (ABC-SMC) framework, permABC exploits the exchangeability of compartments through permutation-based matching, significantly improving computational efficiency. We then develop two further, complementary sequential strategies: Over Sampling, which facilitates early-stage acceptance by temporarily increasing the number of simulated compartments, and Under Matching, which relaxes the acceptance condition by matching only subsets of the data. These techniques allow for robust and scalable inference even in high-dimensional regimes. Through synthetic and real-world experiments — including a hierarchical Susceptible-Infectious-Recover model of the early COVID-19 epidemic across 94 French departments — we demonstrate the practical gains in accuracy and efficiency achieved by our approach.
Salle : A707
Séminaire
Rencontres statistiques
REISACH Alexander (Université Paris Cité)
Le 24/11/2025
De 13:45 à 14:45
Titre : The Case for Time in Causal DAGs
Résumé : Graphical causal models, usually in the form of directed acyclic graphs (DAGs), are a central model class for encoding and reasoning about causal relationships between different quantities. In contrast to other causal models, they do not encode the temporal relationship between variables explicitly. We demonstrate that such nontemporal causal DAGs are ambiguous and obstruct justification of the acyclicity assumption. Assuming that causes precede effects, causal relationships are relative to the time order, and causal DAGs require temporal qualification. We propose a formalization via "composite" causal variables that refer to quantities at one or multiple time points. We emphasize that the acyclicity assumption requires different justifications depending on whether the time order allows cycles. We conclude by discussing implications for the interpretation and applicability of DAGs as causal models.
Salle : P205
Séminaire
Séminaire Analyse-Probabilités
DAVID Noemi (CNRS and LMRS - Université de Rouen)
Le 25/11/2025
De 10:30 à 11:30
Titre : Singular limits in mechanical models of tissue growth
Résumé : Based on the mechanical viewpoint that living tissues exhibit a fluid-like behavior, PDE models inspired by fluid dynamics are now well established as one of the main mathematical tools for the macroscopic description of tissue growth. Depending on the type of tissue, these models link the pressure to the velocity field using either Brinkman’s law (viscoelastic models) or Darcy’s law (porous medium equations, PME). Furthermore, the stiffness of the pressure law plays a crucial role in distinguishing density-based (compressible) models from free-boundary (incompressible) problems, in which the density is saturated. In this talk, I will show how to connect different mechanical models of living tissues through singular limits. In particular, I will discuss the inviscid limit toward the PME, the incompressible limit of the PME leading to free-boundary problems of the Hele-Shaw type, and finally the joint limit.
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
BOINAY Clarisse (INRIA)
Le 27/11/2025
De 17:00 à 18:00
Titre : Detection of anomalies in dynamic graphs with applications in cybersecurity for OT
Résumé : Aggregating instantaneous graphs can achieve approximate independence between the resulting aggregated graphs, a property supported by both (asymptotic) theoretical and (finite sample size) empirical evidence. This justifies the use of a multilayer Poisson-directed Stochastic Block Model (SBM) under the assumption of independence between layers. Within this unusual simplied framework for dynamic graphs, we propose a statistical test for anomaly detection. Furthermore, we extend the model to accommodate variations in the number of nodes over time by employing a missing data paradigm, overpassing in that way main litterature advances which are limited to the number of edges variations. Finally, we demonstrate that initializing the Variational Expectation-Maximization (VEM) algorithm using Singular Value Decomposition (SVD) is effective, even in the presence of missing data.
Salle : A707
Séminaire
GTD Systèmes Dynamiques
LEGUIL Martin (CMLS École Polytechnique)
Le 01/12/2025
De 10:00 à 11:30
Titre : Rigidité des conjugaisons en dynamique hyperbolique
Résumé : On s’intéresse à la question suivante : étant deux systèmes lisses topologiquement conjugués, quand peut-on montrer qu’ils sont en fait conjugués de manière lisse ? Cette question a d’abord été étudiée pour des difféomorphismes du cercle (résultats d’Arnold, Herman, Yoccoz…). Dans ces exposés, nous nous concentrerons sur des systèmes hyperboliques ; dans ce cadre, des obstructions naturelles apparaissent à l’existence d’une conjugaison lisse, portées par les orbites périodiques. Je commencerai par présenter des résultats classiques et quelques idées de leurs preuves, dans le cas des endomorphismes dilatants du cercle (théorème de rigidité de Shub-Sullivan), des difféomorphismes d’Anosov du tore \T^2 (résultats de De la Llave-Marco-Moriyón), et des flots d’Anosov de contact en dimension trois (résultat de Feldman-Ornstein), ainsi que des applications à la rigidité du Spectre Marqué des Longueurs pour des surfaces de courbure négative (théorème de Otal et Croke). Dans une deuxième partie, je présenterai des développements plus récents, dans le cas de flots 3D « Axiom A » de contact (Florio-Leguil), de flots d’Anosov 3D conservatifs (Gogolev-Rodriguez Hertz), et de flots d’Anosov 3D dissipatifs (Gogolev-Leguil-Rodriguez Hertz). Si le temps le permet, je présenterai également des difficultés supplémentaires apparaissant en dimension supérieure (contre-exemples de De la Llave), et des résultats récents de rigidité au voisinage de ces derniers (Gogolev-Leguil).
Salle : P203
Colloque
Colloquium du CEREMADE
BACH Francis (INRIA, ENS & PSL)
Le 02/12/2025
De 15:30 à 16:30
Titre : Denoising diffusion models without diffusions
Résumé : Denoising diffusion models have enabled remarkable advances in generative modeling across various domains. These methods rely on a two-step process: first, sampling a noisy version of the data—an easier computational task—and then denoising it, either in a single step or through a sequential procedure. Both stages hinge on the same key component: the score function, which is closely tied to the optimal denoiser mapping noisy inputs back to clean data. In this talk, I will introduce an alternative perspective on denoising-based sampling that bypasses the need for continuous-time diffusion processes. This framework not only offers a fresh conceptual angle but also naturally extends to discrete settings, such as binary data. Joint work with Saeed Saremi and Ji-Won Park.
Salle : A709
Séminaire
Séminaire des jeunes chercheurs
TOKKA Nicolas (Modal’X, Université Paris-Nanterre & IRIF, Université Paris-Cité)
Le 04/12/2025
De 17:00 à 18:00
Titre : Invitation to (random) planar maps
Résumé : The field of planar maps is relatively young. They were introduced in the 1960s through the work of William T. Tutte. Since then, they have been intensely studied in many directions: in enumerative and bijective combinatorics, topology, probability, algebra, statistical physics, and quantum physics. This talk will be an opportunity to introduce the notion of planar maps and to explore their combinatorial properties. We will also see how they serve as a relevant prototype for defining random geometric spaces. Finally, we will briefly illustrate, through the Ising model, how these random geometries provide an interesting framework for statistical physics.
Salle : A707
Séminaire
Rencontres statistiques
GED François (University of Vienna)
Le 08/12/2025
De 13:45 à 14:45
Titre : Kernel-Smoothed Score in Denoising Diffusions
Résumé : Denoising diffusion models are able to generate realistic and complex data (images, text, molecular structures, ...). However, we still lack a clear theoretical picture of when and why they generalise rather than memorise finite training sets. To probe this, we introduce a simplified model that replaces the empirical score with a mollified score obtained by convolution. This modification induces a two-fold regularisation: (i) an isotropic diffusion that blurs fine, sample-specific features, and (ii) a smoothing along the data manifold that preserves the global structure of the support. Building on this idea, we propose the LED-KDE (Log-Exponential Double-Kernel Density Estimator), a density estimator that, unlike standard KDEs, reduces leakage of mass outside of the data manifold. Using a bias-variance decomposition tied to the mollification, we analyse the empirical score in the small-time, large dataset regime and derive upper bounds on the distance between the true data distribution and the distribution produced by the mollified denoising diffusion. These bounds quantify how mollification improves the generative process and clarify the mechanism by which denoising diffusion models can avoid memorisation and achieve better generalisation. Based on joint work with Franck Gabriel, Maria Han Veiga and Emmanuel Schertzer
Salle : A305
Séminaire
Séminaire Analyse-Probabilités
VANNEUVILLE Hugo (Institut Fourier (Université Grenoble Alpes))
Le 09/12/2025
De 10:30 à 11:30
Titre : Noise sensitivity for percolation
Résumé : Let us consider the hexagonal lattice, let us randomly color each hexagon independently black or white with probability 1/2, and look at percolation events (for example, the event that there is a black path from left to right in a large square). Benjamini, Kalai, and Schramm proved that percolation properties are noise sensitive, which means that if we introduce a ‘noise’ -- even very small -- to the colors of the hexagons, then the percolation events after and before the noise are quasi-independent of each other. In this talk, we would like to propose a ‘robust’ approach -- i.e., one that extends to more general models, for example where the colors are not independent of each other -- to noise sensitivity. Unlike previous approaches, we do not rely on spectral tools but on differential inequalities satisfied by the probabilities of so-called ‘4-arm’ events, which are at the heart of Kesten's work in the 1980s and which we will define. Joint work with Vincent Tassion.
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
MONOD Mélodie (CEREMADE)
Le 11/12/2025
De 17:00 à 18:00
Titre : NeuralSurv: Deep Survival Analysis with Bayesian Uncertainty Quantification
Résumé : We introduce NeuralSurv, the first deep survival model to incorporate Bayesian uncertainty quantification. Our non-parametric, architecture-agnostic framework captures time-varying covariate-risk relationships in continuous time via a novel two-stage data-augmentation scheme, for which we establish theoretical guarantees. For efficient posterior inference, we introduce a mean-field variational algorithm with coordinate-ascent updates that scale linearly in model size. By locally linearizing the Bayesian neural network, we obtain full conjugacy and derive all coordinate updates in closed form. In experiments, NeuralSurv delivers superior calibration compared to state-of-the-art deep survival models, while matching or exceeding their discriminative performance across both synthetic benchmarks and real-world datasets. Our results demonstrate the value of Bayesian principles in data-scarce regimes by enhancing model calibration and providing robust, well-calibrated uncertainty estimates for the survival function.
Salle : A707
Séminaire
Rencontres statistiques
BROGAT-MOTTE Luc (Istituto Italiano di Tecnologia)
Le 15/12/2025
De 13:45 à 14:45
Titre : Learning Controlled Stochastic Differential Equations
Résumé : Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while providing strong learning guarantees for safe and reliable performance. However, existing approaches often focus on simplified scenarios, such as deterministic models, known diffusion, discrete systems, one-dimensional dynamics, or systems constrained by strong structural assumptions such as linearity. This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled stochastic differential equations with non-uniform diffusion. We assume regularity of the coefficients within a Sobolev space, allowing for broad applicability to various dynamical systems in robotics, finance, climate modeling, and biology. Leveraging the Fokker-Planck equation, we split the estimation into two tasks: (a) estimating system dynamics for a finite set of controls, and (b) estimating coefficients that govern those dynamics. We provide strong theoretical guarantees, including finite-sample bounds for \(L^2\), \(L^\infty\), and risk metrics, with learning rates adaptive to coefficients' regularity, similar to those in nonparametric least-squares regression literature. The practical effectiveness of our approach is demonstrated through extensive numerical experiments. Our method is available as an open-source Python library.
Salle : P205
Séminaire
GTD Systèmes Dynamiques
LEGUIL Martin (CMLS École Polytechnique)
Le 15/12/2025
De 10:00 à 11:30
Titre : Rigidité des conjugaisons en dynamique hyperbolique
Résumé : On s’intéresse à la question suivante : étant deux systèmes lisses topologiquement conjugués, quand peut-on montrer qu’ils sont en fait conjugués de manière lisse ? Cette question a d’abord été étudiée pour des difféomorphismes du cercle (résultats d’Arnold, Herman, Yoccoz…). Dans ces exposés, nous nous concentrerons sur des systèmes hyperboliques ; dans ce cadre, des obstructions naturelles apparaissent à l’existence d’une conjugaison lisse, portées par les orbites périodiques. Je commencerai par présenter des résultats classiques et quelques idées de leurs preuves, dans le cas des endomorphismes dilatants du cercle (théorème de rigidité de Shub-Sullivan), des difféomorphismes d’Anosov du tore \T^2 (résultats de De la Llave-Marco-Moriyón), et des flots d’Anosov de contact en dimension trois (résultat de Feldman-Ornstein), ainsi que des applications à la rigidité du Spectre Marqué des Longueurs pour des surfaces de courbure négative (théorème de Otal et Croke). Dans une deuxième partie, je présenterai des développements plus récents, dans le cas de flots 3D « Axiom A » de contact (Florio-Leguil), de flots d’Anosov 3D conservatifs (Gogolev-Rodriguez Hertz), et de flots d’Anosov 3D dissipatifs (Gogolev-Leguil-Rodriguez Hertz). Si le temps le permet, je présenterai également des difficultés supplémentaires apparaissant en dimension supérieure (contre-exemples de De la Llave), et des résultats récents de rigidité au voisinage de ces derniers (Gogolev-Leguil).
Salle : D204
Séminaire
Séminaire Analyse-Probabilités
SALORT Delphine (LJLL, Sorbonne Université)
Le 16/12/2025
De 10:30 à 11:30
Titre : Asymptotic dynamic of neural models with partial diffusion
Résumé : In many biological contexts, one observes Brownian motions that are restricted to certain variables or random movements that differ from classical Brownian motion. Among these mod- els are those involving large populations of interacting neurons. In such models, the variability of neuronal ion channels, which are also subject to random fluctuations, is modeled by diffusion in the conductance variable, while the membrane potential variable remains non-diffusive. Other models focus exclusively on the membrane potential (without conductance) and include an adaptation variable that responds to stimuli received by the neurons. In this case, diffusion is applied to the membrane potential, while the adaptation variable remains non-diffusive. All these phenomena can lead to changes in propagation speed and, in some cases, a significant loss of regularity properties. In this talk, we will explain, using two toy models from neuroscience, how to study the asymptotic properties of these equations and deduce the exponential convergence of the solution toward the stationary state in L^1.
Salle : A711
Séminaire
Séminaire des jeunes chercheurs
GIACOMIN Lydia (King’s College London)
Le 18/12/2025
De 17:00 à 18:00
Titre : Localization in certain disordered quantum spin chains.
Résumé : The phenomenon of localization in disordered systems was first described by Philip W. Anderson, who highlighted the insulating behavior that certain single-particle lattice models display in the presence of strong disorder. Since then, localization phenomena have been studied in depth. While Anderson localization is well-understood at strong disorder (with mathematical proofs achieved for any dimension), the question whether Anderson insulators retain localization properties in the presence of interactions remains open. In this talk, I will present an overview of the current scope of knowledge on this topic (known as many-body localization, or MBL) and highlight a recent result which aims to set a rigorous mathematical framework for the proof of MBL. Using a multi-scale analysis, one can show absence of diffusion for a robust set of interacting 1D spin chain models. The reasoning leading to this result can be extended to hopefully derive a rigorous proof of MBL, an aspect that is left for further work.
Salle : A707
Séminaire
Rencontres statistiques
JAFFARD Sophie (Dresden)
Le 05/01/2026
De 13:45 à 14:45
Titre : Applications of Hawkes processes in biological neural networks.
Résumé : Neurons communicate by generating brief electrical impulses known as spikes. A widely used framework for representing spike trains in a neural network is the multivariate Hawkes process. In this talk, I will present two applications of Hawkes models in biological neural networks. In the first part, I will introduce a biologically plausible spiking neural network model for decision-making tasks, in which neuronal activity is represented using Hawkes processes. We established strong approximation results between this network and drift–diffusion models (DDMs), commonly employed in cognitive science to account for choice behavior and reaction times, which enables to bridge the gap between cognitive and biological models. In the second part, I will describe a new method for inferring neuronal interactions from partially observed spike train data. This method leverages first- and second-order moment statistics of the Hawkes process to reconstruct functional connectivity.
Salle : A306
Séminaire
Séminaire Analyse-Probabilités
GRASSELLI Viviana (IECL - Metz)
Le 27/01/2026
De 10:30 à 11:30
Titre :
Résumé :
Salle : A711
Séminaire
Séminaire Analyse-Probabilités
VAN DEN BOSCH Hanne (Universidad de Chile)
Le 17/02/2026
De 09:00 à 09:00
Titre : TBA
Résumé :
Salle : A711
Séminaire
Séminaire Analyse-Probabilités
SUN Changzhen (CNRS & Laboratoire de Mathématiques de Besançon)
Le 14/04/2026
De 10:30 à 11:30
Titre :
Résumé :
Salle : A711
Séminaire
Séminaire Analyse-Probabilités
AYI Nathalie (LJLL)
Le 19/05/2026
De 10:30 à 11:30
Titre : TBA
Résumé : TBA
Salle : A711