Meta-stability and condensed zero-range processes on finite sets

TL;DR

This paper defines meta-stability for Markov processes on finite sets, provides conditions for it, and demonstrates that certain condensed zero-range processes with decreasing jump rates exhibit meta-stability.

Contribution

It introduces a formal definition of meta-stability and proves that a class of condensed zero-range processes with decreasing jump rates are meta-stable.

Findings

Meta-stability conditions are characterized by capacity and measure estimates in the reversible case.

Condensed zero-range processes with asymptotically decreasing jump rates are proven to be meta-stable.

The paper provides sufficient conditions for meta-stability in finite Markov processes.

Abstract

We propose a definition o meta-stability and obtain sufficient conditions for a sequence of Markov processes on finite state spaces to be meta-stable. In the reversible case, these conditions reduce to estimates of the capacity and the measure of certain meta-stable sets. We prove that a class of condensed zero-range processes with asymptotically decreasing jump rates is meta-stable.