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

First available in Project Euclid: 23 April 2004

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Zentralblatt MATH identifier

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

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


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.

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