Electronic Journal of Probability

Decay of correlations for the hardcore model on the $d$-regular random graph

Nayantara Bhatnagar, Allan Sly, and Prasad Tetali

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 9, 42 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1454682890

Digital Object Identifier
doi:10.1214/16-EJP3552

Mathematical Reviews number (MathSciNet)
MR3485351

Zentralblatt MATH identifier
1342.60160

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
reconstruction threshold hardcore model random regular graph decay of correlations Gibbs measure

Rights
Creative Commons Attribution 4.0 International License.

Citation

Bhatnagar, Nayantara; Sly, Allan; Tetali, Prasad. Decay of correlations for the hardcore model on the $d$-regular random graph. Electron. J. Probab. 21 (2016), paper no. 9, 42 pp. doi:10.1214/16-EJP3552. https://projecteuclid.org/euclid.ejp/1454682890


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