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

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.