Two mathematical tools to analyze metastable stochastic processes

2012/01/18 by Tony Lelièvre, Lelièvre, Tony
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Statistical Mechanics and Entropy #Theoretical and Computational Physics

paper · doi:10.48550/arxiv.1201.3775

openalex publication_date 2012/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present how entropy estimates and logarithmic Sobolev inequalities on the one hand, and the notion of quasi-stationary distribution on the other hand, are useful tools to analyze metastable overdamped Langevin dynamics, in particular to quantify the degree of metastability. We discuss the interest of these approaches to estimate the efficiency of some classical algorithms used to speed up the sampling, and to evaluate the error introduced by some coarse-graining procedures. This paper is a summary of a plenary talk given by the author at the ENUMATH 2011 conference.

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