Metastability in stochastic dynamics of disordered mean-field models

We study a class of Markov chains that describe reversible stochastic dynam ics of a large class of disordered mean field models at low temperatures. O ur main purpose is to give a precise relation between the metastable time s cales in the problem to the properties of the rate functions of the corresp onding Gibbs measures. We derive the analog of the Wentzell Freidlin theory in this case, showings that any transition can be decomposed, with probabi lity exponentially close to one, into a deterministic sequence of "admissib le transitions". For these admissible transitions we give upper and lower b ounds on the expected transition times that differ only by a constant facto r. The distributions of the rescaled transition times are shown to converge to the exponential distribution. We exemplify our results in the context o f the random field Curie-Weiss model.