Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

À l'occasion de la visite de Insuk Seo (Seoul National University, Corée du Sud) et Jungkyoung Lee (Korea Institue for Advanced Study, Corée du Sud), une mini-école d'hiver sur le thème de la métastabilité aura lieu au LMRS les jeudi 11 janvier 2024 après-midi et lundi 15 janvier 2024 matin.

Insuk Seo et Jungkyoung Lee proposeront un cours en deux parties.

jeudi 11 janvier 2024

14h-15h

Benoît Dagallier (Courant Institute, New York) - Fluctuations et corrélations pour l'exclusion simple faiblement asymétrique sur un tore soumise à un courant atypique

(exposé du Groupe de travail en Probabilités, Théorie Ergodique et Systèmes Dynamiques)

15h15-16h45

Insuk Seo (Seoul National University, Corée du Sud) - Recent methods in the mathematical study of metastability (Partie 1)

lundi 15 janvier 2024

9h15-10h45

Joungkyoung Lee (Korea Institue for Advanced Study, Corée du Sud) - Recent methods in the mathematical study of metastability (Partie 2)

Résumé du cours.

In this lecture series, we review recent developments in the quantitative analysis of metastable behavior. The first lecture we mildly introduce the examples of models exhibiting metastability (e.g., Langevin dynamics, spin systems and interacting particle systems). Then, we also briefly review classic potential theoretic approach of Bovier, Eckhoff, Gayrard and Klein and explain how this approach can be extended to the non-reversible models. We remark that these methods are based on the estimation of the so-called capacity between metastable sets which is carried out via variational principles such as Dirichlet principle. We will also explain alternative approach to estimate the capacity that does not use variational principles and hence is particularly suitable in the analysis of non-reversible case. In the second lecture, we explain the Markov chain model reduction method called martingale approach in the quantitative analysis of metastability developed by Beltran and Landim. We first connect this approach with the potential theoretic computations explained in the first lecture. Then, we introduce completely brand new methodology based on the analysis of certain form of resolvent equations. This new method does not use potential theory.