# Fredrickson-Andersen one spin facilitated model out of equilibrium

Abstract : We consider the Fredrickson and Andersen one spin facilitated model (FA1f) on an infinite connected graph with polynomial growth. Each site with rate one refreshes its occupation variable to a filled or to an empty state with probability $p\in[0,1]$ or $q=1-p$ respectively, provided that at least one of its nearest neighbours is empty. We study the non-equilibrium dynamics started from an initial distribution $\nu$ different from the stationary product $p$-Bernoulli measure $\mu$. We assume that, under $\nu$, the mean distance between two nearest empty sites is uniformly bounded. We then prove convergence to equilibrium when the vacancy density $q$ is above a proper threshold $\bar q<1$. The convergence is exponential or stretched exponential, depending on the growth of the graph. In particular it is exponential on $\bbZ^d$ for $d=1$ and stretched exponential for $d>1$. Our result can be generalized to other non cooperative models.
Type de document :
Pré-publication, Document de travail
2012
Domaine :

https://hal.archives-ouvertes.fr/hal-00705252
Contributeur : Cristina Toninelli <>
Soumis le : jeudi 7 juin 2012 - 11:01:21
Dernière modification le : lundi 29 mai 2017 - 14:27:03

### Identifiants

• HAL Id : hal-00705252, version 1
• ARXIV : 1205.4584

### Citation

Oriane Blondel, Nicoletta Cancrini, Fabio Martinelli, Cyril Roberto, Cristina Toninelli. Fredrickson-Andersen one spin facilitated model out of equilibrium. 2012. 〈hal-00705252〉

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