Perfect simulation and finitary coding for multicolor systems with interactions of infinite range

2008/09/20 by Antonio Galves, A. Galves, N. L. Garcia +5 · 1 citation
Mathematics · Physics and Astronomy · #28D99 #60K35 #82B20 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:28D99 #msc:60K35 #msc:82B20

paper · pdf · doi:10.48550/arxiv.0809.3494

openalex publication_date 2008/09/20 · arxiv created 2009/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a particle system on Z^d with finite state space and interactions of infinite range. Assuming that the rate of change is continuous and decays sufficiently fast, we introduce a perfect simulation algorithm for the stationary process. The algorithm follows from a representation of the multicolor system as a finitary coding from a sequence of independent uniform random variables. This implies that the process is exponentially ergodic. The basic tool we use is a representation of the infinite range change rates as a mixture of finite range change rates.

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