Mathematical Physics/Probability Theory
On the distribution of the overlaps at given disorder
Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 303-306.

We prove a rigorous version of the following heuristic statement: if, in a spin glass model, the extended Ghirlanda–Guerra identities are valid, at given disorder the distribution of the overlap of two configurations is discrete, and its support (the smallest closed set that carries this distribution) is non-random.

Nous prouvons une version rigoureuse du fait suivant. Dans un modèle de verres de spins qui satisfait les identités de Ghirlanda–Guerra générales, à désordre donné, la distribution du recouvrement de deux configurations est discrète, et son support est non-aléatoire.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.06.014
Parisi, Giorgio 1; Talagrand, Michel 2

1 Center for Statistical Mechanics and Complexity, INFM Roma “la Sapienza”, Piazzale Aldo Morro 2, 00185 Roma, Italy
2 Équipe d'Analyse de l'Institut Mathématique, 4, place Jussieu, 75230 Paris cedex 05, France
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Parisi, Giorgio; Talagrand, Michel. On the distribution of the overlaps at given disorder. Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 303-306. doi : 10.1016/j.crma.2004.06.014. http://www.numdam.org/articles/10.1016/j.crma.2004.06.014/

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