Two mathematical tools to analyze metastable stochastic processes
For researchers studying metastable stochastic processes, this provides a theoretical framework to analyze sampling algorithms and coarse-graining, but it is a summary of a talk with no new results.
The paper presents entropy estimates, logarithmic Sobolev inequalities, and quasi-stationary distributions as tools to analyze metastable overdamped Langevin dynamics, quantifying metastability and evaluating algorithm efficiency and coarse-graining errors.
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.