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Front evolution of the Fredrickson-Andersen one spin facilitated model

Abstract : The Fredrickson-Andersen one spin facilitated model (FA-1f) on 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 ¯ 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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Contributor : Aurelia Deshayes <>
Submitted on : Friday, October 26, 2018 - 12:30:36 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:59 PM
Document(s) archivé(s) le : Sunday, January 27, 2019 - 1:39:28 PM


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  • HAL Id : hal-01740818, version 2
  • ARXIV : 1803.08761


Oriane Blondel, Aurelia Deshayes, Cristina Toninelli. Front evolution of the Fredrickson-Andersen one spin facilitated model. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2019, 24 (1), pp.1-32. ⟨hal-01740818v2⟩



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