Exponential \(\Phi \)-Mixing Implies Exponential \(\Psi \)-Mixing For Markov Fields On Bounded Degree Graphs

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2026年7月7日

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Elias Zimmermann

摘要

We show that for non-degenerate k-Markovian random fields with finite state space over a bounded degree graph with exponential growth rate , uniform -mixing with exponential decay rate implies uniform -mixing with exponential decay rate . As an application we obtain exponential -mixing for Gibbs fields on regular trees arising from finite range potentials such as the Ising model at low inverse temperature or the Potts model with sufficiently many spin states.