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2016 Decay of correlations for the hardcore model on the $d$-regular random graph
Nayantara Bhatnagar, Allan Sly, Prasad Tetali
Electron. J. Probab. 21: 1-42 (2016). DOI: 10.1214/16-EJP3552

Abstract

A key insight from statistical physics about spin systems on random graphs is the central role played by Gibbs measures on trees. We determine the local weak limit of the hardcore model on random regular graphs upto a density for the largest independent set that is bounded by and goes asymptotically to the condensation threshold. We show that the hardcore measure converges in probability locally in a strong sense to the free boundary condition Gibbs measure on the tree. As a consequence we show that the reconstruction threshold on the random graph, indicative of the onset of point to set spatial correlations, is equal to the reconstruction threshold on the $d$-regular tree for which we determine precise asymptotics. We expect that our methods will generalize to a wide range of spin systems for which the second moment method holds.

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Nayantara Bhatnagar. Allan Sly. Prasad Tetali. "Decay of correlations for the hardcore model on the $d$-regular random graph." Electron. J. Probab. 21 1 - 42, 2016. https://doi.org/10.1214/16-EJP3552

Information

Received: 31 May 2014; Accepted: 30 December 2015; Published: 2016
First available in Project Euclid: 5 February 2016

zbMATH: 1342.60160
MathSciNet: MR3485351
Digital Object Identifier: 10.1214/16-EJP3552

Subjects:
Primary: 60K35

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