Reconstruction Threshold for the Hardcore Model
نویسندگان
چکیده
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 λ < (ln 2 − o(1)) ln k 2 ln ln k improving the previous best bound of λ < e − 1. This is almost tight as reconstruction is known to hold when λ > (e+ o(1)) ln 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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