WIAS Preprint No. 146, (1995)

An almost sure large deviation principle for the Hopfield model



Authors

  • Bovier, Anton
  • Gayrard, Véronique

2010 Mathematics Subject Classification

  • 60F10 82B44 82C32

Keywords

  • Hopffield model, neural networks, self-averaging, large deviations

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 lim sup M(N)/N = 0. In this case the rate function is independent of the disorder for almost all realizations of the patterns.

Appeared in

  • Ann. Probab., 24 (1996), pp. 1444-1475

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