Duality for general attractive spin systems with applications in one dimension
type: Item
instance of: scholarly article
title: Duality for general attractive spin systems with applications in one dimension
zbMATH Open document ID: 0604.60098
published in: The Annals of Probability
publication date: 1986-01-01T00:00:00Z
review text: Duality has become an important tool in the theory of interacting spin systems in \({\mathbb{Z}}^ d\). In this paper a new version of dual processes is introduced, whose paths take their values in the collection of finite subsets instead of the elements of \({\mathbb{Z}}^ d\). They promise to be applicable to more general classes of processes than the previous ones, which were limited to special cases. As an example, the author generalizes results of \textit{R. Durrett} and \textit{D. Griffeath} [ibid. 11, 1-15 (1983; Zbl 0508.60080)], which they proved for the nearest neighbour one-dimensional contact process to all attractive nearest neighbour one-dimensional spin systems with critical behaviour. These results concern exponential convergence starting from all 1's to an equilibrium measure, which has exponentially decaying correlation functions.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 3976064
zbMATH Keywords: interacting spin systems
zbMATH Keywords: exponential convergence
zbMATH Keywords: exponentially decaying correlation functions
author: Lawrence F. Gray
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992522
OpenAlex ID: W2081719560
DOI: 10.1214/AOP/1176992522
description: scientific article; zbMATH DE number 3976064