A strong correlation inequality for contact processes and oriented percolation
type: Item
instance of: scholarly article
title: A strong correlation inequality for contact processes and oriented percolation
zbMATH Open document ID: 0890.60094
DOI: 10.1016/S0304-4149(97)00009-4
published in: Stochastic Processes and their Applications
publication date: 1998-03-29T00:00:00Z
review text: The strengthening of the positive correlation inequality \(\nu (A\cap B)\nu (A\cup B) \geq \nu (A)\nu (B)\) is proved for the following two cases. The extinction probability \(\nu (A)\) for the contact process on a countable set \(S\) with initial state \(A\subset S\), or equivalently, for \(\nu (A)=\nu _\infty (\{\eta ;\eta _A\equiv 0\})\) with \(\nu _\infty \) being the upper invariant measure of the contact process. The same inequality is independently proved for \(\nu \) being the extinction probability of an oriented percolation which can be viewed as a discrete time version of the one-dimensional contact process.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82C22
zbMATH DE Number: 1134829
zbMATH Keywords: contact process
zbMATH Keywords: oriented percolation
zbMATH Keywords: extinction probability
zbMATH Keywords: correlation inequality
author: Vladimir Belitsky
author: Pablo A. Ferrari
author: Norio Konno
author: Thomas M. Liggett
reviewed by: Petr Holický
MaRDI profile type: Publication
cites work: Oriented percolation in two dimensions
cites work: Q4040029
cites work: Contact interactions on a lattice
cites work: A correlation inequality for Markov processes in partially ordered state spaces
cites work: Q4857326
cites work: Q5185817
cites work: The survival of one-dimensional contact processes in random environments
cites work: Q4848559
cites work: Q5665539
full work available at URL: s0304-4149(97)00009-4
OpenAlex ID: W1973958689
description: scientific article; zbMATH DE number 1134829