Reconstruction threshold for the hardcore model

Authors:
Nayantara Bhatnagar;Allan Sly;Prasad Tetali
Affiliations:
Hebrew University, Microsoft Research, Georgia Tech;Hebrew University, Microsoft Research, Georgia Tech;Hebrew University, Microsoft Research, Georgia Tech
Venue:
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Year:
2010

Citing 8
Cited 1

Random Regular Graphs of Non-Constant Degree: Independence and Chromatic Number

Combinatorics, Probability and Computing
Fast mixing for independent sets, colorings and other models on trees

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A second threshold for the hard-core model on a Bethe lattice

Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
Optimal phylogenetic reconstruction

Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels

FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic Barriers from Phase Transitions

FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Reconstruction for the Potts model

Proceedings of the forty-first annual ACM symposium on Theory of computing
Phase transition for the mixing time of the Glauber dynamics for coloring regular trees

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms

On independent sets in random graphs

Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we consider the reconstruction problem on the tree for the hardcore model. We determine new bounds for the nonreconstruction regime on the k-regular tree showing nonreconstruction when λ o(1))ln2k/2ln lnk improving the previous best bound of λ e - 1. This is almost tight as reconstruction is known to hold when λ (e+o(1)) ln2 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.