Séminaire des jeunes chercheurs

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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 Analyse-Probabilités

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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

Rencontres statistiques

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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 Analyse-Probabilités

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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