Random graph approach to Gibbs processes with pair interaction
type: Item
instance of: scholarly article
title: Random graph approach to Gibbs processes with pair interaction
zbMATH Open document ID: 0726.60046
published in: Acta Applicandae Mathematicae
publication date: 1991-01-01T00:00:00Z
review text: A translation invariant Gibbs point process for a pair potential of a special type is constructed. The distribution of this process is obtained as the equilibrium distribution of a Markov chain of point processes in \({\mathbb{R}}^ d\) which are represented as a sequence of subsets of the set of vertices of a special random graph. This embedding permits to analyse Markov chain as well as to suggest a stochastic construction of the equilibrium. The constructions are carried out under the condition of ergodicity of the chain given in terms of the ``absence of percolation'' in the graph.
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B31
zbMATH DE Number: 4199174
zbMATH Keywords: Palm distribution
zbMATH Keywords: Markov chain imbedding in a random graph
zbMATH Keywords: translation invariant Gibbs point process
zbMATH Keywords: pair potential
zbMATH Keywords: equilibrium distribution of a Markov chain
zbMATH Keywords: condition of ergodicity
zbMATH Keywords: absence of percolation
author: Rouben V. Ambartsumian
reviewed by: S. Poghosyan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4199174