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


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Limit Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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