An exposition to information percolation for the Ising model
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 4, pp. 745-761.

La percolation de l’information est une nouvelle méthode pour analyser les systèmes de spins stochastiques à travers la classification et le contrôle des amas de flots d’information dans des tranches d’espace-temps. Elle fournit des estimées fines de mélange (transition abrupte dans une fenêtre d’ordre O(1)) pour le modèle d’Ising sur d jusqu’à la température critique, ainsi que des résultats sur l’influence des conditions initiales sur le mélange. Dans cet article de présentation, nous appliquons cette méthode à des réseaux (plus généralement, sur tout graphe localement fini et transitif) à très haute température.

Information percolation is a new method for analyzing stochastic spin systems through classifying and controlling the clusters of information-flow in the space-time slab. It yielded sharp mixing estimates (cutoff with an O(1)-window) for the Ising model on d up to the critical temperature, as well as results on the effect of initial conditions on mixing. In this expository note we demonstrate the method on lattices (more generally, on any locally-finite transitive graph) at very high temperatures.

DOI : 10.5802/afst.1462
Lubetzky, Eyal 1 ; Sly, Allan 2

1 Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA.
2 Department of Statistics, UC Berkeley, Berkeley, CA 94720, USA.
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Lubetzky, Eyal; Sly, Allan. An exposition to information percolation for the Ising model. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 4, pp. 745-761. doi : 10.5802/afst.1462. http://archive.numdam.org/articles/10.5802/afst.1462/

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