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October 2000 Exponential inequalities and convergence of moments in the replica-symmetric regime of the Hopfield model
Michel Talagrand
Ann. Probab. 28(4): 1393-1469 (October 2000). DOI: 10.1214/aop/1019160495

Abstract

In a previous work,we proved the validity ofthe replica-symmetric solution for the Hop field model in a nontrivial domain of parameters. This was done at the accuracy ofthe LLN In a somewhat larger domain, we obtain a description at the level ofthe CLT, or, in the terminology of physics, we calculate the fluctuations around the mean field. This is obtained by refining the tools we developed for a rigorous use of the cavity method and proving new a priori estimates about the “localization”of the Gibbs measure.

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Michel Talagrand. "Exponential inequalities and convergence of moments in the replica-symmetric regime of the Hopfield model." Ann. Probab. 28 (4) 1393 - 1469, October 2000. https://doi.org/10.1214/aop/1019160495

Information

Published: October 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1043.82036
MathSciNet: MR1813831
Digital Object Identifier: 10.1214/aop/1019160495

Subjects:
Primary: 60G99 , 82D30

Keywords: Hopfield model , replica-symmetric solution , Spin glass

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 4 • October 2000
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