Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

The reduction method, the loop erased exit path, and the metastability of the biased majority vote process on a torus.

Auteur(s):

Code(s) de Classification MSC:

Résumé: The reduction method provides an algorithm to compute large deviation estimates of (possibly non reversible) Markov processes with exponential transition rates. It replaces the original graph minimisation equations of Freidlin and Wentzell by more tractable path minimisation problems. When applied to study the metastability of the dynamics, it gives a large deviation principle for the loop erased exit path from the metastable state. We apply this technique to a biased majority vote process generalising the one studied in Chen \cite{[2]}. We show that this non reversible dynamics has a two well potential with a unique metastable state, we give an upper bound for its relaxation time, and show that for small enough values of the bias the exit path is typically different at low temperature from the typical exit paths of the Ising model.

Mots Clés: Finite Markov chains with exponential transitions; Metastability; Biased Majority Vote Process; Large Deviations

Date: 1999-01-08

Prépublication numéro: PMA-478

Dernière révision : septembre 1999, fichier PMA-478-bis.dvi.gz compressé avec gzip. (La version d'origine reste reliée au titre de cette fiche.)
(Last revision, dating from september 1999, the original manuscript is still linked to the title of this page.)