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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 82B44 Disordered systems (random Ising models, random Schrodinger operators, etc.)
- 60G70 Extreme value theory; extremal processes
- 60K35 Interacting random processes; statistical mechanics type models; percolation theory, See also {82B43, 82C43}

**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