Exponential $$\Phi $$-Mixing Implies Exponential $$\Psi $$-Mixing For Markov Fields On Bounded Degree Graphs
Abstract
Abstract We show that for non-degenerate k -Markovian random fields with finite state space over a bounded degree graph with exponential growth rate "Equation missing" , uniform "Equation missing" -mixing with exponential decay rate "Equation missing" implies uniform "Equation missing" -mixing with exponential decay rate "Equation missing" . As an application we obtain exponential "Equation missing" -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.
Fields of Study & Subjects
Markov Chains and Monte Carlo Methods
Stochastic processes and statistical mechanics
stochastic dynamics and bifurcation
Publication details
- Journal / source
- Journal of Statistical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 193
- Issue
- 7
- Publication date
- 7 July 2026
- Language
- EN