Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A symmetric entropy bound on the non-reconstruction regime of Markov
  chains on Galton-Watson trees   We give a criterion of the form Q(d)c(M)<1 for the non-reconstructability of
tree-indexed q-state Markov chains obtained by broadcasting a signal from the
root with a given transition matrix M. Here c(M) is an explicit function, which
is convex over the set of M's with a given invariant distribution, that is
defined in terms of a (q-1)-dimensional variational problem over symmetric
entropies. Further Q(d) is the expected number of offspring on the
Galton-Watson tree. This result is equivalent to proving the extremality of the
free boundary condition-Gibbs measure within the corresponding Gibbs-simplex.
Our theorem holds for possibly non-reversible M and its proof is based on a
general Recursion Formula for expectations of a symmetrized relative entropy
function, which invites their use as a Lyapunov function.
  In the case of the Potts model, the present theorem reproduces earlier
results of the authors, with a simplified proof, in the case of the symmetric
Ising model (where the argument becomes similar to the approach of Pemantle and
Peres) the method produces the correct reconstruction threshold), in the case
of the (strongly) asymmetric Ising model where the Kesten-Stigum bound is known
to be not sharp the method provides improved numerical bounds.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg