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Un théorème limite pour les covariances des spins dans le modèle de Sherrington--Kirkpatrick avec champ externe

Albert Hanen
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Abstract

On étudie la covariance (pour la mesure de Gibbs) des spins en deux sites dans le cas d'un modèle de Sherrington--Kirkpatrick avec champ externe; lorsque le nombre de sites du modèle tend vers l'infini, une évaluation asymptotique des moments d'ordre $p$ de cette covariance permet d'obtenir un théorème limite faible avec une loi limite en général non gaussienne. We study the covariance (for Gibbs measure) of spins at two sites in the case of a Sherrington--Kirkpatrick model with an external field. When the number of sites of the model grows to infinity, an asymptotic evaluation of the $p$ moments of that covariance allows us to obtain a weak limit theorem, with a generally non-Gaussian limit law.

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Albert Hanen. 2007-03-27. Un théorème limite pour les covariances des spins dans le modèle de Sherrington--Kirkpatrick avec champ externe. https://doi.org/10.1214/009117906000000665

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