An almost sure large deviation principle for the Hopfield model

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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