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.
Publié le : 1996-07-14
Classification:
Hopfield model,
neural networks,
self-averaging,
large deviations,
60F10,
82B44,
82C32
@article{1065725188,
author = {Bovier, Anton and Gayrard, V\'eronique},
title = {An almost sure large deviation principle for the Hopfield
model},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1444-1475},
language = {en},
url = {http://dml.mathdoc.fr/item/1065725188}
}
Bovier, Anton; Gayrard, Véronique. An almost sure large deviation principle for the Hopfield
model. Ann. Probab., Tome 24 (1996) no. 2, pp. 1444-1475. http://gdmltest.u-ga.fr/item/1065725188/