A Resolvent Approach to Metastability
C. Landim, D. Marcondes, I. Seo
TL;DR
This paper establishes a precise criterion for metastability in Markov chains using resolvent equations and demonstrates its application to reversible zero-range processes, advancing understanding of metastable behavior in stochastic systems.
Contribution
It introduces a resolvent-based condition for metastability and applies it to prove metastability in reversible zero-range processes.
Findings
Provides a necessary and sufficient condition for metastability.
Proves metastability of reversible, critical zero-range processes.
Links resolvent solutions to metastable behavior.
Abstract
We provide a necessary and sufficient condition for the metastability of a Markov chain, expressed in terms of a property of the solutions of the resolvent equation. As an application of this result, we prove the metastability of reversible, critical zero-range processes starting from a configuration.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Stochastic processes and statistical mechanics · Stochastic processes and financial applications