Tunneling and Metastability of continuous time Markov chains

TL;DR

This paper introduces a new framework for understanding metastability in continuous-time Markov chains, providing conditions based on capacity and stationary measures, especially for reversible processes.

Contribution

It offers a novel definition of metastability and provides sufficient conditions for sequences of Markov processes to exhibit metastable behavior.

Findings

New definition of metastability for Markov processes

Sufficient conditions involving capacity and stationary measure

Applicable to reversible Markov chains

Abstract

We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the capacity and of the stationary measure of the metastable states.