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July 1996 An almost sure large deviation principle for the Hopfield model
Anton Bovier, Véronique Gayrard
Ann. Probab. 24(3): 1444-1475 (July 1996). DOI: 10.1214/aop/1065725188

Abstract

We prove a large deviation principle for the finite-dimensional marginals of the Gibbs distribution of the macroscopic "overlap" parameters in the Hopfield model in the case where the number of random "patterns" M , as a function of the system size N, satisfies lim sup $M(N) /N =0$. In this case, the rate function is independent of the disorder for almost all realizations of the patterns.

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Anton Bovier. Véronique Gayrard. "An almost sure large deviation principle for the Hopfield model." Ann. Probab. 24 (3) 1444 - 1475, July 1996. https://doi.org/10.1214/aop/1065725188

Information

Published: July 1996
First available in Project Euclid: 9 October 2003

zbMATH: 0871.60022
MathSciNet: MR1411501
Digital Object Identifier: 10.1214/aop/1065725188

Subjects:
Primary: 60F10, 82B44, 82C32

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 3 • July 1996
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