## The Annals of Probability

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

J. Theodore Cox

#### 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

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