The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels
Probability
2011-09-07 v1 Computational Complexity
Populations and Evolution
Abstract
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.
Cite
@article{arxiv.math/0604366,
title = {The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels},
author = {Christian Borgs and Jennifer Chayes and Elchanan Mossel and Sebastien Roch},
journal= {arXiv preprint arXiv:math/0604366},
year = {2011}
}