The central limit theorem and the problem of equivalence of ensembles
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In this paper we show that the local limit theorem is a consequence of the integral central limit theorem in the case of a Gibbs random field ξt,tεZν corresponding to a finite range potential.
We apply this theorem to show that the equivalence between Gibbs and canonical ensemble is a consequence of the integral central limit theorem and of very weak conditions on decrease of correlations.
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