On a representation of Gibbs measure for R.E.M.

Marie Kratz (1, 2, 3) , P. Picco (4, 5)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 MATISSE - UMR 8595 - Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques
4 CPT - Centre de Physique Théorique - UMR 6207
5 CPT - Centre de Physique Théorique - UMR 7332

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.

Mots clés: Extremes; Finite Markov processes; Gaussian r.v.; Order Statistics; Random Spin Systems; Uniform r.v.; Gaussian r.v; Uniform r.v

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Systèmes dynamiques [math.DS]; Probabilités [math.PR]

Marie Kratz, P. Picco. On a representation of Gibbs measure for R.E.M.. The Annals of Applied Probability, 2004, 14, pp.1. ⟨hal-00171270⟩