preprint · Electronic Journal of Probability · 2016

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

Nayantara Bhatnagar, Allan Sly, Prasad Tetali

Cited by 1Open 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.

Cite this paper

APA 7

Bhatnagar, N., Sly, A., & Tetali, P. (2016). Decay of correlations for the hardcore model on the $d$-regular random graph. Electronic Journal of Probability, 21(none). https://doi.org/10.1214/16-ejp3552

MLA 9

Bhatnagar, Nayantara, et al. “Decay of correlations for the hardcore model on the $d$-regular random graph.” Electronic Journal of Probability, vol. 21, no. none, 2016, https://doi.org/10.1214/16-ejp3552.

Chicago

Bhatnagar, Nayantara, Allan Sly, and Prasad Tetali. 2016. “Decay of correlations for the hardcore model on the $d$-regular random graph.” Electronic Journal of Probability 21 (none). https://doi.org/10.1214/16-ejp3552.

Harvard

Bhatnagar, N., Sly, A. and Tetali, P. (2016) ‘Decay of correlations for the hardcore model on the $d$-regular random graph’, Electronic Journal of Probability, 21(none). Available at: https://doi.org/10.1214/16-ejp3552.

BibTeX

@misc{bhatnagar2016decay,
  title = {{Decay of correlations for the hardcore model on the $d$-regular random graph}},
  author = {Bhatnagar, Nayantara and Sly, Allan and Tetali, Prasad},
  journal = {Electronic Journal of Probability},
  volume = {21},
  number = {none},
  year = {2016},
  doi = {10.1214/16-ejp3552}
}

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