Open Access
July, 1987 Decomposition of Binary Random Fields and Zeros of Partition Functions
Charles M. Newman
Ann. Probab. 15(3): 1126-1130 (July, 1987). DOI: 10.1214/aop/1176992085


Let $\delta_c(X)$ denote the maximum $d$ in $\lbrack 0, \frac{1}{2}\rbrack$ such that a binary Gibbs random field $X$ can be decomposed as the modulo 2 sum of two independent binary fields, one of which is independent Bernoulli (white binary noise) of weight $d$. In a recent paper, Hajek and Berger showed, under modest assumptions, that $\delta_c > 0$. We point out here that the decomposition of $X$ is related to the classic statistical mechanics problem of determining zero-free regions of partition functions. A theorem of Ruelle is then applied to obtain improved estimates for $\delta_c$.


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Charles M. Newman. "Decomposition of Binary Random Fields and Zeros of Partition Functions." Ann. Probab. 15 (3) 1126 - 1130, July, 1987.


Published: July, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0646.60058
MathSciNet: MR893918
Digital Object Identifier: 10.1214/aop/1176992085

Primary: 60G60
Secondary: 60B15 , 82A05 , 94A34

Keywords: Decomposition , distortion theory , Gibbs distributions , Partition functions , Random fields , Zeros

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 3 • July, 1987
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