The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels
<|reference_start|>The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric Binary Channels: 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.<|reference_end|>
@article{borgs2006the,
    title={The Kesten-Stigum Reconstruction Bound Is Tight for Roughly Symmetric
  Binary Channels},
    author={Christian Borgs, Jennifer Chayes, Elchanan Mossel, Sebastien Roch},
    journal={arXiv preprint arXiv:math/0604366},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0604366},
    primaryClass={math.PR cs.CC q-bio.PE}
}