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 factor. The distributions of the 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 26 November 1998 / Revised version: 21 March 2000 / Published online: 14 December 2000
Rights and permissions
About this article
Cite this article
Bovier, A., Eckhoff, M., Gayrard, V. et al. Metastability in stochastic dynamics of disordered mean-field models. Probab Theory Relat Fields 119, 99–161 (2001). https://doi.org/10.1007/PL00012740
Issue Date:
DOI: https://doi.org/10.1007/PL00012740