An almost sure large deviation principle for the Hopfield model

Anton Bovier; Véronique Gayrard

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An almost sure large deviation principle for the Hopfield model

Anton Bovier·Véronique Gayrard

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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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Anton Bovier, Véronique Gayrard. 1995-04-03. An almost sure large deviation principle for the Hopfield model. https://arxiv.org/abs/cond-mat/9504003

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