A representation of Gibbs measure for the random energy model

2004/05/01 by Marie Kratz, Marie F. Kratz, Pierre Picco
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:62G30 #msc:62G32. #msc:82B44

paper · pdf · doi:10.1214/105051604000000053

published as Annals of Applied Probability 2004, Vol. 14, No. 2, 651-677

openalex publication_date 2004/05/01 · arxiv created 2004/05/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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