02-264 A. Bovier (WIAS), I. Kurkova (Univ. Paris 6)

Derrida's Generalized Random Energy models 2: Gibbs measures and probability cascades (506K, PS) Jun 13, 02

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Abstract. This is the second in a series of three papers in which we present a full rigorous analysis of Derrida's Generalized Random Energy Models (GREM). In this paper we still consider only models with finitely many levels. In this context we present two ways to prove the convergence of the Gibbs measures (in a suitable representation). The first is direct and shows convergence to the probability cascades introduced by Ruelle. The second approach is indirect and use the so-called Ghirlanda-Guerra identities, that allow to control the distribution of the Gibbs measures via recursive identities for their moments.

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