- 95-188 Anton Bovier, V\'eronique Gayrard
- An almost sure large deviation principle for the Hopfield model
Apr 3, 95
(auto. generated ps),
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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.