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June, 1975 Markov Random Fields on an Infinite Tree
Frank Spitzer
Ann. Probab. 3(3): 387-398 (June, 1975). DOI: 10.1214/aop/1176996347


Phase transition is studied on the infinite tree $T_N$ in which every point has exactly $N + 1$ neighbors. For every assignment of conditional probabilities which are invariant under graph isomorphism there is a Markov chain with these conditional probabilities and the main results ascertain for which ones of these chains there are other Markov random fields with the same conditional probabilities.


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Frank Spitzer. "Markov Random Fields on an Infinite Tree." Ann. Probab. 3 (3) 387 - 398, June, 1975.


Published: June, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0313.60072
MathSciNet: MR378152
Digital Object Identifier: 10.1214/aop/1176996347

Primary: 60J10
Secondary: 60K35 , 82A25

Keywords: Markov chains on infinite trees , Markov random fields , phase transition

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 3 • June, 1975
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