A correlation inequality for the symmetric exclusion process
type: Item
instance of: scholarly article
title: A correlation inequality for the symmetric exclusion process
zbMATH Open document ID: 0642.60105
published in: The Annals of Probability
publication date: 1988-01-01T00:00:00Z
review text: Let \((\eta_ t)_{t\geq 0}\) denote the symmetric exclusion process on \(X=\{0,1\}^ S\) where S is finite or countable. The author shows that for any disjoint subsets A, B of S \[ (*)\quad P(\prod_{x\in A\cup B}\eta_ t(x)=1)\leq P(\prod_{x\in A}\eta_ t(x)=1)P(\prod_{x\in B}\eta_ t(x)=1),\quad t\geq 0. \] This extends a well-known correlation inequality [cf. \textit{T. M. Liggett}, ``Interacting particle systems'' (1985; Zbl 0559.60078)]. Restricting himself to the case in which \(S=Z^ d\) and the transition matrix is symmetric, translation invariant and irreducible, the author derives a pointwise ergodic theorem using (*).
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4046869
zbMATH Keywords: symmetric exclusion process
zbMATH Keywords: correlation inequality
zbMATH Keywords: translation invariant
author: Enrique Daniel Andjel
reviewed by: Klaus Schürger
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991782
OpenAlex ID: W2014545772
DOI: 10.1214/AOP/1176991782
description: scientific article; zbMATH DE number 4046869