A Martingale approach to metastability

TL;DR

This paper introduces a new martingale-based method to analyze metastability in continuous-time Markov chains, focusing on mixing and relaxation times instead of direct jumps among metastable states.

Contribution

It extends previous approaches by replacing the jump-based assumptions with conditions on mixing and relaxation times, broadening the applicability of metastability analysis.

Findings

New martingale approach for metastability analysis

Conditions on mixing and relaxation times replace jump assumptions

Broader applicability to continuous-time Markov chains

Abstract

We presented in \cite{bl2,bl7} an approach to derive the metastable behavior of continuous-time Markov chains. We assumed in these articles that the Markov chains visit points in the time scale in which it jumps among the metastable sets. We replace this condition here by assumtpions on the mixing times and on the relaxation times of the chains reflected at the boundary of the metastable sets.