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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60F10 Large deviations
- 60Jxx Markov processes
- 82C05 Classical dynamic and nonequilibrium statistical mechanics

**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.)*