2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/27249We 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.31pp; Plain-TeX, hardcopy available on request from bovier@iaas-berlin.d400.deCondensed Mattertext