Metastability in stochastic dynamics of disordered mean-field models
Bovier, A. ; Eckhoff, M. ; Gayrard, V. ; Klein, M.
arXiv, 9811331 / Harvested from arXiv
Text on arXiv
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.
Publié le : 1998-11-24
Classification:  Condensed Matter - Disordered Systems and Neural Networks,  Mathematical Physics 
@article{9811331,
     author = {Bovier, A. and Eckhoff, M. and Gayrard, V. and Klein, M.},
     title = {Metastability in stochastic dynamics of disordered mean-field models},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9811331}
}

Bovier, A.; Eckhoff, M.; Gayrard, V.; Klein, M. Metastability in stochastic dynamics of disordered mean-field models. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9811331/