STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 卷:119 |
On the purity of the free boundary condition Potts measure on random trees | |
Article | |
Formentin, Marco2  Kulske, Christof1  | |
[1] Univ Groningen, Dept Math & Comp Sci, NL-9747 AC Groningen, Netherlands | |
[2] Univ Padua, Dipartimento Matemat Pura & Applicata, I-35121 Padua, Italy | |
关键词: Potts model; Gibbs measures; Random tree; Reconstruction problem; Free boundary condition; | |
DOI : 10.1016/j.spa.2009.03.008 | |
来源: Elsevier | |
【 摘 要 】
We consider the free boundary condition Gibbs measure of the Potts model on a random tree. We provide an explicit temperature interval below the ferromagnetic transition temperature for which this measure is extremal, improving older bounds of Mossel and Peres. In information theoretic language extremality of the Gibbs measure corresponds to non-reconstructability for symmetric q-ary channels. The bounds for the corresponding threshold value of the inverse temperature are optimal for the Ising model and differ from the Kesten Stigum bound by only 1.50% in the case q = 3 and 3.65% for q = 4, independently of d. Our proof uses an iteration of random boundary entropies from the outside of the tree to the inside, along with a symmetrization argument. (C) 2009 Elsevier B.V. All rights reserved.
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