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Erdős-Rényi laws for Gibbs measures

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Abstract

Can one detect a phase transition from a single, large sample of a Gibbs measure? What information does one get on the other Gibbs distributions with the same potential? We approach these questions via Erdős-Rényi laws. In particular we prove almost-sure limit theorems for sets of empirical distributions of sub-samples of the given one: for suitable sub-samples size this set converges to the set of stationary Gibbs measures. Moreover we formulate Erdős-Rényi laws for general families of random variables with suitable large deviation principles.

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Communicated by M. Aizenman

URA CNRS 756 (Centre de Mathématiques Appliquées, Ecole Polytechnique) et 1321 (Statistique et Modèles Aléatoires, Université Paris 7)

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Comets, F.M. Erdős-Rényi laws for Gibbs measures. Commun.Math. Phys. 162, 353–369 (1994). https://doi.org/10.1007/BF02102022

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  • DOI: https://doi.org/10.1007/BF02102022

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