## Electronic Journal of Probability

### Front evolution of the Fredrickson-Andersen one spin facilitated model

#### Abstract

The Fredrickson-Andersen one spin facilitated model (FA-1f) on $\mathbb Z$ belongs to the class of kinetically constrained spin models (KCM). Each site refreshes with rate one its occupation variable to empty (respectively occupied) with probability $q$ (respectively $p=1-q$), provided at least one nearest neighbor is empty. Here, we study the non equilibrium dynamics of FA-1f started from a conﬁguration entirely occupied on the left half-line and focus on the evolution of the front, namely the position of the leftmost zero. We prove, for $q$ larger than a threshold $\bar q<1$, a law of large numbers and a central limit theorem for the front, as well as the convergence to an invariant measure of the law of the process seen from the front.

#### Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 1, 32 pp.

Dates
Accepted: 16 November 2018
First available in Project Euclid: 4 January 2019

https://projecteuclid.org/euclid.ejp/1546571126

Digital Object Identifier
doi:10.1214/18-EJP246

Mathematical Reviews number (MathSciNet)
MR3903501

Zentralblatt MATH identifier
1406.60127

#### Citation

Blondel, Oriane; Deshayes, Aurelia; Toninelli, Cristina. Front evolution of the Fredrickson-Andersen one spin facilitated model. Electron. J. Probab. 24 (2019), paper no. 1, 32 pp. doi:10.1214/18-EJP246. https://projecteuclid.org/euclid.ejp/1546571126

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