Anton Bovier, Veronique Gayrard
AN ALMOST SURE CENTRAL LIMIT THEOREM FOR THE HOPFIELD MODEL
(157K, PS)
ABSTRACT. We prove a central limit theorem
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
$\lim_{N\uparrow\infty} M(N)/N=0$, without any
assumptions on the speed of convergence.
The covariance matrix of the limiting gaussian distributions is
diagonal and independent of the disorder for almost
all realizations of the patterns.