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Exact thresholds for Ising–Gibbs samplers on general graphs

Mossel, Elchanan; Sly, Allan


We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising model on general graphs. We show that if (d − 1)tanhβ < 1, then there exists a constant C such that the discrete time mixing time of Gibbs samplers for the ferromagnetic Ising model on any graph of n vertices and maximal degree d, where all interactions are bounded by β, and arbitrary external fields are bounded by Cn log n. Moreover, the spectral gap is uniformly bounded away from 0 for all such...[Show more]

CollectionsANU Research Publications
Date published: 2013
Type: Journal article
Source: The Annals of Probability
DOI: 10.1214/11-AOP737


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