Colloque
Colloquium du CEREMADE
BOUCHAUD Jean-Philippe (CFM)
Le 05/05/2026
De 15:30 à 16:30
Titre : Large covariance matrices, eigenvector overlaps & “fleeting modes”: a (free) RMT approach
Résumé : We will how discuss free Random Matrix Theory allows one to understand the overlap of the eigenvectors of noisy covariance matrices with their underlying "true" counterparts, with direct applications to financial data analysis. Using matrix subordination laws derived from replica methods, we compute explicit overlaps between eigenvectors of pure and noise-perturbed matrices in both additive and multiplicative noise scenarios. These universal results—independent of specific matrix distributions—enable remarkable "large dimension miracles": optimal estimators of unknown covariance matrices can be constructed knowing only observed data, and statistical tests for stationarity can be performed without knowing the true underlying correlation structure. We demonstrate practical applications to portfolio optimization through non-linear shrinkage estimators and introduce "fleeting modes"—a novel diagnostic test identifying unstable eigenvector directions driven by market microstructure and behavioral effects. Finally, we explore time-dependent correlations in financial markets, revealing how principal regression analysis combined with RMT reveals which macroeconomic factors systematically influence asset correlations across market regimes.
Salle : A709
Séminaire
Groupe de travail Probabilites
TBC ()
Le 07/05/2026
De 14:00 à 15:15
Titre : TBC (Attention Thursday)
Résumé :
Salle : D205
Séminaire
Séminaire Jeunes chercheurs
SPHABMIXAY Sixtine (CEREMADE)
Le 07/05/2026
De 17:00 à 18:00
Titre : Adaptive estimation in regression for discretized functional data
Résumé : My presentation will focus on functional data, that is, data taking the form of functions. In practice, such data are never observed continuously, but rather in a discretized and often noisy form. I will specifically examine the impact of this discretization on estimation in the scalar-on-function linear model. My approach first consists in reconstructing the curves from the discrete observations, and then estimating the model using a penalized regression method with model selection. I will present theoretical results, in particular oracle inequalities and convergence rates, which highlight the role of the number of observation points. Finally, an application to energy consumption data will illustrate these results.
Salle : A707
Séminaire
Séminaire Analyse-Probabilités
HAYASHI Kohei (Université d’Osaka)
Le 12/05/2026
De 10:30 à 11:30
Titre : Degree-preserving processes and their hydrodynamics
Résumé : We consider a class of large-scale interacting systems with one conservation law satisfying the “degree-preserving property,” and study the classification of their invariant measures and their hydrodynamic limits. Under a few basic conditions, we show that if the generator of the process preserves the degree of polynomials of the state variables up to two, then the marginals of any product invariant measure of the process must belong to one of six specific distributions, which is called the Morris class. In particular, we introduce a new model whose invariant measure is given by the generalized hyperbolic secant distribution. Additionally, under the same conditions, we show that the classical heat equation is always derived as the hydrodynamic limit equation from generic degree-preserving processes. This talk is based on a joint work with C. Francheschini, P. Gonçalves and M. Sasada.
Salle : A711
Séminaire
GTD Systemes Dynamiques
SAUZIN David (CNRS - Laboratoire Temps Espace)
Le 13/05/2026
De 10:15 à 11:45
Titre : Explicit linearization of multi-dimensional germs and vector fields through Ecalle's tree expansions
Résumé : We provide explicit formulas of non-recursive type for the linearizing transformations of a non-resonant analytic germ of diffeomorphism at a fixed point or a non-resonant analytic germ of vector field at a singular point, in any complex dimension. The formal expressions we obtain rely on a part of Ecalle's tree-based combinatorics called ``armould calculus" and they have the same shape for dynamical systems with discrete or continuous time. They allow us to recover in a straightforward manner, under Bruno's arithmetical condition, the best known estimates for the domains of convergence of the analytic linearizing changes of variables in terms of the value of the Bruno series.
Salle : C515
Séminaire
Séminaire Analyse-Probabilités
AYI Nathalie (LJLL)
Le 19/05/2026
De 10:30 à 11:30
Titre : Large Population Limit for Interacting Particle Systems on Weighted Graphs
Résumé : When studying interacting particle systems, two distinct categories emerge: indistinguishable systems, where particle identity does not influence system dynamics, and non-exchangeable systems, where particle identity plays a significant role. One way to conceptualize these second systems is to see them as particle systems on weighted graphs. In this talk, we focus on the latter category. Recent developments in graph theory have raised renewed interest in understanding large population limits in these systems. Two main approaches have emerged: graph limits and mean-field limits. While mean-field limits were traditionally introduced for indistinguishable particles, they have been extended to the case of non-exchangeable particles recently. In this presentation, we introduce several models, mainly from the field of opinion dynamics, for which rigorous convergence results as N tends to infinity have been obtained. We also clarify the connection between the graph limit approach and the mean-field limit one. The works discussed draw from several papers, some co-authored with Nastassia Pouradier Duteil and David Poyato.
Salle : A711
Séminaire
Groupe de travail Probabilites
TBC ()
Le 20/05/2026
De 14:00 à 15:15
Titre : TBC
Résumé :
Salle : D205
Séminaire
Groupe de travail Probabilites
MARINI Elisa ()
Le 03/06/2026
De 14:00 à 15:15
Titre : TBC
Résumé :
Salle : D205
Séminaire
Groupe de travail Probabilites
TBC ()
Le 17/06/2026
De 14:00 à 15:15
Titre : TBC
Résumé :
Salle : D205