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

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.