The generalized Parisi formula

Michel Talagrand

doi:10.1016/S1631-073X(03)00268-1

Probability Theory/Mathematical Physics

The generalized Parisi formula
[La formule de Parisi généralisée]

Présenté par : Yves Meyer

Michel Talagrand ¹

¹ Équipe d'analyse de l'institut mathématique, 4, place Jussieu, 75230 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 337 (2003) no. 2, pp. 111-114.

Abstract (VO)
Résumé

For a large class of Gaussian Hamiltonians, we use Guerra's interpolation scheme to show that at any temperature the free energy of the corresponding spin-glass system is asymptotically given by Parisi's formula. This class includes the Sherrington–Kirkpatrick model, the p-spin interaction model for even p, and many others.

Pour une large classe d'Hamiltoniens Gaussiens, nous utilisons la méthode d'interpolation de Guerra pour montrer qu'à toute température l'énergie libre du verre spin correspondant est donnée par la formule de Parisi. Cette classe comprend le modèle de Sherrington–Kirkpatrick, le modèle à p-spin pour p pair, et bien d'autres.

Reçu le : 2003-05-26
Accepté le : 2003-05-27
Publié le : 2003-06-28

DOI : 10.1016/S1631-073X(03)00268-1

Affiliations des auteurs :

Michel Talagrand ¹

¹ Équipe d'analyse de l'institut mathématique, 4, place Jussieu, 75230 Paris cedex 05, France

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Michel Talagrand. The generalized Parisi formula. Comptes Rendus. Mathématique, Volume 337 (2003) no. 2, pp. 111-114. doi : 10.1016/S1631-073X(03)00268-1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00268-1/

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