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July, 1987 A Decomposition Theorem for Binary Markov Random Fields
Bruce Hajek, Toby Berger
Ann. Probab. 15(3): 1112-1125 (July, 1987). DOI: 10.1214/aop/1176992084


Consider a binary Markov random field whose neighbor structure is specified by a countable graph with nodes of uniformly bounded degree. Under a minimal assumption we prove a decomposition theorem to the effect that such a Markov random field can be represented as the nodewise modulo 2 sum of two independent binary random fields, one of which is white binary noise of positive weight. Said decomposition provides the information theorist with an exact expression for the per-site rate-distortion function of the random field over an interval of distortions not exceeding this weight. We mention possible implications for communication theory, probability theory and statistical physics.


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Bruce Hajek. Toby Berger. "A Decomposition Theorem for Binary Markov Random Fields." Ann. Probab. 15 (3) 1112 - 1125, July, 1987.


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

zbMATH: 0626.60045
MathSciNet: MR893917
Digital Object Identifier: 10.1214/aop/1176992084

Primary: 60G60
Secondary: 60K35 , 94A34

Keywords: Gibbs random field , Ising model , Markov random field , rate-distortion function

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 3 • July, 1987
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