Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Derrida's Generalized Random Energy models 1: Poisson cascades and extremal processes.


Code(s) de Classification MSC:

Résumé: This is the first of a series of three papers in which we present a full rigorous analysis of a class of spin glass models introduces by Derrida under the name of Generalized Random Energy Models (GREM). They are based on Gaussian random processes on the hypercube $\{-1,1\}^N$ with a hierarchical correlation structure. In this first paper we prove some result concerning the convergence of the extremal process to Poisson cascade processes which will form the basis of the analysis of the Gibbs measures to be presented in the sequel.

Mots Clés: Gaussian processes ; extreme values ; order statistics ; generalized random energy model ; spin glasses ; Poisson cascades

Date: 2002-05-17

Prépublication numéro: PMA-727

Pdf file : PMA-727.pdf