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arXiv · 1004.3531

Reconstruction Threshold for the Hardcore Model

Nayantara Bhatnagar·Allan Sly·Prasad Tetali
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Abstract

In this paper we consider the reconstruction problem on the tree for the hardcore model. We determine new bounds for the non-reconstruction regime on the k-regular tree showing non-reconstruction when lambda < (ln 2-o(1))ln^2(k)/(2 lnln(k)) improving the previous best bound of lambda < e-1. This is almost tight as reconstruction is known to hold when lambda> (e+o(1))ln^2(k). We discuss the relationship for finding large independent sets in sparse random graphs and to the mixing time of Markov chains for sampling independent sets on trees.

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Nayantara Bhatnagar, Allan Sly, Prasad Tetali. 2010-04-20. Reconstruction Threshold for the Hardcore Model. https://arxiv.org/abs/1004.3531

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