2016/12/08 by Nick Crawford, Wojciech De Roeck, Crawford, N. +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1612.02620
openalex publication_date 2016/12/08 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
In this paper, we prove a general result concerning finite-range, attractive interacting particle systems on \-1, 1\ℤd. If the particle system has a unique stationary measure and, in a precise sense, relaxes to this stationary measure at an exponential rate then any small perturbation of the dynamics also has a unique stationary measure to which it relaxes at an exponential rate. To augment this result, we study the particular case of Glauber dynamics for the Ising model. We show that for any non-zero external field the dynamics converges to its unique invariant measure at an exponential rate. Previously, this was only known for β