The Annals of Probability

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.

Article information

Source
Ann. Probab., Volume 35, Number 1 (2007), 141-179.

Dates
First available in Project Euclid: 19 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1174324126

Digital Object Identifier
doi:10.1214/009117906000000665

Mathematical Reviews number (MathSciNet)
MR2303946

Zentralblatt MATH identifier
1115.82037

Subjects
Primary: 82D30: Random media, disordered materials (including liquid crystals and spin glasses) 60G15: Gaussian processes 60F05: Central limit and other weak theorems

Keywords
SK models Gibbs measure overlaps central limit theorem

Citation

Hanen, Albert. Un théorème limite pour les covariances des spins dans le modèle de Sherrington–Kirkpatrick avec champ externe. Ann. Probab. 35 (2007), no. 1, 141--179. doi:10.1214/009117906000000665. https://projecteuclid.org/euclid.aop/1174324126


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References

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