The Annals of Applied Probability

A representation of Gibbs measure for the random energy model

Marie F. Kratz and Pierre Picco

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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.

Article information

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

Dates
First available in Project Euclid: 23 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1082737106

Digital Object Identifier
doi:10.1214/105051604000000053

Mathematical Reviews number (MathSciNet)
MR2052897

Zentralblatt MATH identifier
1070.82016

Subjects
Primary: 62G30: Order statistics; empirical distribution functions 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
Secondary: 62G32: Statistics of extreme values; tail inference

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

Citation

Kratz, Marie F.; Picco, Pierre. A representation of Gibbs measure for the random energy model. Ann. Appl. Probab. 14 (2004), no. 2, 651--677. doi:10.1214/105051604000000053. https://projecteuclid.org/euclid.aoap/1082737106


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