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math.PRFeb 10, 2021
authors
  • Insuk Seo
arXiv abstractPDF
paper

Generalized Dirichlet and Thomson Principles and Their Applications

arXiv:2102.05538

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.

arXiv comment110 pages, 3 figures

References in corpus (13)

  • Tunneling and Metastability of continuous time Markov chains
  • Metastability in Glauber dynamics in the low-temperature limit: Beyond exponential asymptotics
  • Kramers' law: Validity, derivations and generalisations
  • Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States
  • Metastability for general dynamics with rare transitions: escape time and critical configurations
  • Metastability in the reversible inclusion process
  • Metastability of the two-dimensional Blume-Capel model with zero chemical potential and small magnetic field
  • Sum of exit times in a series of two metastable states
  • Metastable Markov chains: from the convergence of the trace to the convergence of the finite-dimensional distributions
  • Metastability of the two-dimentional Blume-Capel model with zero chemical potential and small magnetic field on a large torus
  • Non-reversible Metastable Diffusions with Gibbs Invariant Measure II: Markov Chain Convergence
  • An Eyring-Kramers law for slowly oscillating bistable diffusions
  • Second Time Scale of the Metastability of Reversible Inclusion Processes
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