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. © 1977 Springer-Verlag.
The central limit theorem and the problem of equivalence of ensembles / R. L., Dobrushin; Tirozzi, Benedetto. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 54:2(1977), pp. 173-192. [10.1007/bf01614136]
The central limit theorem and the problem of equivalence of ensembles
TIROZZI, Benedetto
1977
Abstract
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. © 1977 Springer-Verlag.File allegati a questo prodotto
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