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2019 Front evolution of the Fredrickson-Andersen one spin facilitated model
Oriane Blondel, Aurelia Deshayes, Cristina Toninelli
Electron. J. Probab. 24(none): 1-32 (2019). DOI: 10.1214/18-EJP246

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.

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Oriane Blondel. Aurelia Deshayes. Cristina Toninelli. "Front evolution of the Fredrickson-Andersen one spin facilitated model." Electron. J. Probab. 24 1 - 32, 2019. https://doi.org/10.1214/18-EJP246

Information

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

Subjects:
Primary: 60K35
Secondary: 60J27

JOURNAL ARTICLE
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