A representation of Gibbs measure for the random energy model

A representation of Gibbs measure for the random energy model

Marie F. Kratz and Pierre Picco

Source: Ann. Appl. Probab. Volume 14, Number 2 (2004), 651-677.

Abstract

In this work we consider a problem related to the equilibrium statistical mechanics of spin glasses, namely the study of the Gibbs measure of the random energy model. For solving this problem, new results of independent interest on sums of spacings for i.i.d. Gaussian random variables are presented. Then we give a precise description of the support of the Gibbs measure below the critical temperature.

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Primary Subjects: 62G30, 82B44

Secondary Subjects: 62G32

Keywords: Extremes; Gaussian r.v.; order statistics; random spin systems; uniform r.v.

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aoap/1082737106
Digital Object Identifier: doi:10.1214/105051604000000053
Mathematical Reviews number (MathSciNet): MR2052897
Zentralblatt MATH identifier: 02100749

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