Open Access
2019 Front evolution of the Fredrickson-Andersen one spin facilitated model
Oriane Blondel, Aurelia Deshayes, Cristina Toninelli
Electron. J. Probab. 24: 1-32 (2019). DOI: 10.1214/18-EJP246


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.


Download Citation

Oriane Blondel. Aurelia Deshayes. Cristina Toninelli. "Front evolution of the Fredrickson-Andersen one spin facilitated model." Electron. J. Probab. 24 1 - 32, 2019.


Received: 22 March 2018; Accepted: 16 November 2018; Published: 2019
First available in Project Euclid: 4 January 2019

zbMATH: 1406.60127
MathSciNet: MR3903501
Digital Object Identifier: 10.1214/18-EJP246

Primary: 60K35
Secondary: 60J27

Keywords: contact process , coupling , invariant measure , Kinetically constrained models

Vol.24 • 2019
Back to Top