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Decay of correlations under Dobrushin's uniqueness condition and its applications

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Abstract

An estimate on the correlation of functionals of Gibbs fields satisfying Dobrushin's uniqueness condition is given. As a consequence a result of Gross saying that the truncated pair correlation function decays in the same weighted summability sense as the potential can be extended to the whole Dobrushin uniqueness region. Applications to the central limit theorem and the second derivative of the pressure are also given.

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Authors and Affiliations

  1. Mathematics Department, ETH Zentrum, CH-8092, Zürich, Switzerland

    H. Künsch

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  1. H. Künsch
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Communicated by E. Lieb

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Künsch, H. Decay of correlations under Dobrushin's uniqueness condition and its applications. Commun.Math. Phys. 84, 207–222 (1982). https://doi.org/10.1007/BF01208568

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  • DOI: https://doi.org/10.1007/BF01208568

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