Communications in Mathematical Physics

, Volume 54, Issue 2, pp 173–192 | Cite as

The central limit theorem and the problem of equivalence of ensembles

  • R. L. Dobrushin
  • Brunello Tirozzi
Article

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 ,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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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • R. L. Dobrushin
    • 1
  • Brunello Tirozzi
    • 2
  1. 1.Institute of Problems of Information TransmissionAk. Nauk. U.R.S.S.MoscowUSSR
  2. 2.Istituto Matematico dell'Università di CamerinoCamerinoItaly

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