Berman-Konsowa principle for reversible Markov jump processes

TL;DR

This paper extends the Berman-Konsowa principle to reversible Markov jump processes on Polish spaces, providing a variational formula for capacity that aids in estimating crossover times in metastable systems.

Contribution

It proves a version of the Berman-Konsowa principle for Markov jump processes, offering a new variational approach to capacity estimation in complex stochastic systems.

Findings

Provides a variational formula for capacity between disjoint sets.

Introduces two versions involving probability measures and finite flows.

Enhances tools for estimating crossover times in metastable systems.

Abstract

In this paper we prove a version of the Berman-Konsowa principle for reversible Markov jump processes on Polish spaces. The Berman-Konsowa principle provides a variational formula for the capacity of a pair of disjoint measurable sets. There are two versions, one involving a class of probability measures for random finite paths from one set to the other, the other involving a class of finite unit flows from one set to the other. The Berman-Konsowa principle complements the Dirichlet principle and the Thomson principle, and turns out to be especially useful for obtaining sharp estimates on crossover times in metastable interacting particle systems.