Exponential convergence for attractive reversible subcritical nearest particle systems
type: Item
instance of: scholarly article
title: Exponential convergence for attractive reversible subcritical nearest particle systems
zbMATH Open document ID: 0847.60083
DOI: 10.1016/0304-4149(95)00048-C
author: Thomas Mountford
published in: Stochastic Processes and their Applications
publication date: 1996-09-30T00:00:00Z
review text: The exponential convergence to zero of the probability that a site is occupied is proved for a nearest particle system on integers. The flip rates are defined, for a configuration \(\gamma\) at site \(x\), by \(c(x, \gamma) = 1\) if \(\gamma (x) = 1\) and \(c(x, \gamma) = \beta (l_x, r_x) \geq 0\) if \(\gamma (x) = 0\), where \(l_x\) and \(r_x\) are the distances to the first occupied site at the left, or at the right side to \(x\), respectively. A special form of \(\beta\) is investigated and the system is supposed to be reversible, attractive, Feller, and subcritical (the only invariant measure is \(\gamma = 0\) with probability one). Some uniform bound on the values \(\beta (l,r)\) is needed.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60B10
zbMATH DE Number: 828752
zbMATH Keywords: nearest particle system
zbMATH Keywords: flip rates
zbMATH Keywords: reversibility
zbMATH Keywords: exponential convergence
reviewed by: Petr Holický
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 828752