Perfect simulation of infinite range Gibbs measures and coupling with their finite range approximations

2009/04/30 by Antonio Galves, Eva Loecherbach, Enza Orlandi · 1 citation
Mathematics · Physics and Astronomy · #math.PR #math-ph #math.MP #msc:82B20 #msc:60K35 #msc:60G60 #msc:62M40

paper · pdf · doi:10.1007/s10955-009-9881-3

arxiv created 2009/09/30 · arxiv updated 2015/05/13

Abstract

In this paper we address the questions of perfectly sampling a Gibbs measure with infinite range interactions and of perfectly sampling the measure together with its finite range approximations. We solve these questions by introducing a perfect simulation algorithm for the measure and for the coupled measures. The algorithm works for general Gibbsian interaction under requirements on the tails of the interaction. As a consequence we obtain an upper bound for the error we make when sampling from a finite range approximation instead of the true infinite range measure.

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