Bounded, attractive and repulsive Markov specifications on trees and on the one-dimensional lattice
type: Item
instance of: scholarly article
title: Bounded, attractive and repulsive Markov specifications on trees and on the one-dimensional lattice
zbMATH Open document ID: 0585.60056
DOI: 10.1016/0304-4149(85)90213-3
author: Stan Zachary
published in: Stochastic Processes and their Applications
publication date: 1985-01-01T00:00:00Z
review text: On a regular \((d+1)\)-tree, where \(d+1\) edges meet at each vertex, the author studies the problem of existence and uniqueness of Markov random fields for a given specification, which is supposed to be given by a symmetric translation invariant positive function, defined on pairs of nearest neighbor sites. A boundedness condition yields the existence. The uniqueness problem is discussed for attractive and repulsive specifications. For \(d=1\), the author is able to reduce some more general cases to \textit{H. Kesten}'s uniqueness result [Ann. Probab. 4, 557-569 (1976; Zbl 0367.60080)].
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 3938171
zbMATH Keywords: infinite trees
zbMATH Keywords: existence and uniqueness of Markov random fields
MaRDI profile type: Publication
full work available at URL: 0304-4149(85)90213-3
OpenAlex ID: W1980700367
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description: scientific article; zbMATH DE number 3938171