Generalized Dirichlet and Thomson Principles and Their Applications

TL;DR

This paper explores the potential theory of Markov processes, including non-reversible ones, and connects it to analyzing the metastability of stochastic systems, providing theoretical insights and applications.

Contribution

It introduces generalized Dirichlet and Thomson principles and discusses their applications in the study of metastability in Markov processes.

Findings

Extended potential theory to non-reversible Markov processes.

Established new variational principles for metastability analysis.

Connected theoretical principles with practical stochastic process analysis.

Abstract

This article is a lecture note on the potential theory of (possibly non-reversible) Markov processes and on the connection of this theory with quantitative analysis of the metastability of stochastic processes.