Metastability in stochastic dynamics of disordered mean-field models
Abstract
We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of the corresponding Gibbs measures. We derive the analog of the Wentzell-Freidlin theory in this case, showing that any transition can be decomposed, with probability exponentially close to one, into a deterministic sequence of ``admissible transitions''. For these admissible transitions we give upper and lower bounds on the expected transition times that differ only by a constant. The distribution rescaled transition times are shown to converge to the exponential distribution. We exemplify our results in the context of the random field Curie-Weiss model.
Keywords
Cite
@article{arxiv.cond-mat/9811331,
title = {Metastability in stochastic dynamics of disordered mean-field models},
author = {A. Bovier and M. Eckhoff and V. Gayrard and M. Klein},
journal= {arXiv preprint arXiv:cond-mat/9811331},
year = {2016}
}
Comments
73pp, AMSTEX