Berman-Konsowa Principle for Reversible Markov Jump Processes

#### S. Jansen, F. den Hollander

2016, v.22, №3, 409-442

ABSTRACT

In this paper we prove a version of the Berman\tire Konsowa principle for reversible
Markov jump processes on Polish spaces. The Berman\tire 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\tire 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.

Keywords: reversible Markov jump processes, electric networks, potential theory, capacity, Dirichlet principle, Thomson principle, Berman\tire Konsowa principle