In Markov process, an extremal reversible measure is an extremal invariant measure

2023/08/14 by Hiroki Yagisita, Yagisita, Hiroki
Mathematics · Physics and Astronomy · #FOS: Mathematics #General Mathematics (math.GM) #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2312.14816

openalex publication_date 2023/08/14 · openalex created_date 2023/12/26 · openalex updated_date 2026/07/28

Abstract

We consider a discrete-time temporally-homogeneous conservative Markov process. We show that extremality of reversible measure implies extremality of invariant measure. Using analogue of Dirichlet form, we modify a proof that in stochastic Ising model (Glauber dynamics), an extreme Gibbs state is an extreme invariant measure.

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