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The central limit theorem and the problem of equivalence of ensembles

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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 ξ t ,tεZ ν 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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Authors and Affiliations

  1. Institute of Problems of Information Transmission, Ak. Nauk. U.R.S.S., Moscow, USSR

    R. L. Dobrushin

  2. Istituto Matematico dell'Università di Camerino, I-62032, Camerino, Italy

    Brunello Tirozzi

Authors
  1. R. L. Dobrushin
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  2. Brunello Tirozzi
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Additional information

Communicated by G. Gallavotti

Research supported by a C.N.R.-Ak. Nauk. U.R.S.S. fellowship

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Dobrushin, R.L., Tirozzi, B. The central limit theorem and the problem of equivalence of ensembles. Commun.Math. Phys. 54, 173–192 (1977). https://doi.org/10.1007/BF01614136

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  • DOI: https://doi.org/10.1007/BF01614136

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