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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Galves, A., Löcherbach, E. & Orlandi, E. Perfect Simulation of Infinite Range Gibbs Measures and Coupling with Their Finite Range Approximations. J Stat Phys 138, 476–495 (2010). https://doi.org/10.1007/s10955-009-9881-3
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DOI: https://doi.org/10.1007/s10955-009-9881-3