An almost sure large deviation principle for the Hopfield model

1995/04/03 by Anton Bovier, Bovier, Anton, Véronique Gayrard +1
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #cond-mat

paper · pdf · doi:10.48550/arxiv.cond-mat/9504003

31pp; Plain-TeX, hardcopy available on request from [email protected]

arxiv created 1995/04/03 · arxiv updated 2009/11/30

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 \limsup M(N)/N=0. In this case the rate function (or free energy as a function of the overlap parameters) is independent of the disorder for almost all realization of the patterns and given by an explicit variational formula.

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