Electronic Journal of Probability
- Electron. J. Probab.
- Volume 24 (2019), paper no. 1, 32 pp.
Front evolution of the Fredrickson-Andersen one spin facilitated model
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.
Electron. J. Probab., Volume 24 (2019), paper no. 1, 32 pp.
Received: 22 March 2018
Accepted: 16 November 2018
First available in Project Euclid: 4 January 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
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