An almost sure large deviation principle for the Hopfield model

Details An almost sure large deviation principle for the Hopfield model An almost sure large deviation principle for the Hopfield model

1995-04-03

arxiv.org/abs/cond-mat/9504003v1

Physics

Condensed Matter

31pp; Plain-TeX, hardcopy available on request from bovier@iaas-berlin.d400.de

Scientific paper

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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