The Annals of Probability

An Alternate Proof of a Theorem of Kesten Concerning Markov Random Fields

J. Theodore Cox

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Abstract

Let $S$ be a countable set, $Q$ a strictly positive matrix on $S \times S, \mathscr{G}(Q)$ the set of one-dimensional Markov random fields taking values in $S$ determined by $Q$. In this paper a short proof of Kesten's sufficient condition for $\mathscr{G}(Q) = \phi$ is presented.

Article information

Source
Ann. Probab. Volume 7, Number 2 (1979), 377-378.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995095

Digital Object Identifier
doi:10.1214/aop/1176995095

Mathematical Reviews number (MathSciNet)
MR525061

Zentralblatt MATH identifier
0395.60096

JSTOR
links.jstor.org

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Markov random field entrance law

Citation

Cox, J. Theodore. An Alternate Proof of a Theorem of Kesten Concerning Markov Random Fields. Ann. Probab. 7 (1979), no. 2, 377--378. doi:10.1214/aop/1176995095. https://projecteuclid.org/euclid.aop/1176995095


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