Electronic Journal of Probability

Front evolution of the Fredrickson-Andersen one spin facilitated model

Oriane Blondel, Aurelia Deshayes, and Cristina Toninelli

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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

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

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Digital Object 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

kinetically constrained models invariant measure coupling contact process

Creative Commons Attribution 4.0 International License.


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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