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Metastability in stochastic dynamics of disordered mean-field models

A. Bovier·M. Eckhoff·V. Gayrard·M. Klein
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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.

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A. Bovier, M. Eckhoff, V. Gayrard, M. Klein. 1999-05-20. Metastability in stochastic dynamics of disordered mean-field models. https://arxiv.org/abs/cond-mat/9811331

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