The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels

Details The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels

2006-04-17

arxiv.org/abs/math/0604366v1

Mathematics

Probability

Scientific paper

We establish the exact threshold for the reconstruction problem for a binary asymmetric channel on the b-ary tree, provided that the asymmetry is sufficiently small. This is the first exact reconstruction threshold obtained in roughly a decade. We discuss the implications of our result for Glauber dynamics, phylogenetic reconstruction, and so-called ``replica symmetry breaking'' in spin glasses and random satisfiability problems.

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