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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Article dans une revue
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2019, 24 (1), pp.1-32
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https://hal.archives-ouvertes.fr/hal-01740818
Contributeur : Aurelia Deshayes <>
Soumis le : vendredi 26 octobre 2018 - 12:30:36
Dernière modification le : mardi 19 mars 2019 - 01:23:27
Document(s) archivé(s) le : dimanche 27 janvier 2019 - 13:39:28

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fa1f_front_cor.pdf
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  • HAL Id : hal-01740818, version 2
  • ARXIV : 1803.08761

Citation

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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