Disagreement percolation in the study of Markov fields
type: Item
instance of: scholarly article
title: Disagreement percolation in the study of Markov fields
zbMATH Open document ID: 0814.60096
author: Christian Maes
author: Jacob van den Berg
published in: The Annals of Probability
publication date: 1995-06-13T00:00:00Z
review text: The influence of the boundary conditions on the state of a Markov lattice field is studied in terms of disagreement percolation. This is done by means of the connection between two Markov field realizations corresponding to different boundary conditions. The constructed connection permit to obtain a new uniqueness condition for Gibbs measure on \(\mathbb{Z}^ d\), \(\sum^ n_{k=0} a^ k/k! < 1/(1 - p_ c)\), where \(p_ c\) is the site percolation threshold for the lattice \(\mathbb{Z}^ d\), \((n + 1)\) is the state number of the considered lattice Gibbs system and \(a = \lambda T\).
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B43
Mathematics Subject Classification ID: 82B05
Mathematics Subject Classification ID: 82B26
zbMATH DE Number: 681381
zbMATH Keywords: percolation
zbMATH Keywords: Markovian field
zbMATH Keywords: boundary condition
zbMATH Keywords: Gibbs measure
zbMATH Keywords: uniqueness condition
reviewed by: Yu. P. Virchenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988728
OpenAlex ID: W1998959913
DOI: 10.1214/AOP/1176988728
description: scientific article; zbMATH DE number 681381