An almost sure large deviation principle for the Hopfield model
- Bovier, Anton
- Gayrard, Véronique
2010 Mathematics Subject Classification
- 60F10 82B44 82C32
- Hopffield model, neural networks, self-averaging, large deviations
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.
- Ann. Probab., 24 (1996), pp. 1444-1475