Anton Bovier, V\'eronique Gayrard
An almost sure large deviation principle for the Hopfield model
(326K, PS)

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.