Travelling wave structure of the one dimensional contact process
type: Item
instance of: scholarly article
title: Travelling wave structure of the one dimensional contact process
zbMATH Open document ID: 0626.60104
DOI: 10.1016/0304-4149(87)90195-5
author: Errico Presutti
author: A. Galves
published in: Stochastic Processes and their Applications
publication date: 1987-01-01T00:00:00Z
review text: We consider the one dimensional supercritical contact process with initial configurations having infinitely many particles to the left of the origin and finitely many ones to its right. We study the space time structure of the process. In particular we prove that the law of the process shifted by \(\alpha\) t (t being the time and \(\alpha\) the drift of edge) converges weakly to a \[ - \] mixture of the two extremal invariant measures for the supercritical contact process. We then show that [even] conditioning on the position of the edge, the distribution of the particles to its left is given by \({\tilde \mu}\), the unique invariant measure as seen from the edge. An interpretation of the above results in terms of a discrete particle description of a one dimensional travelling wave is then discussed.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4018083
zbMATH Keywords: local central limit theorem
zbMATH Keywords: supercritical contact process
zbMATH Keywords: invariant measures
zbMATH Keywords: travelling wave
MaRDI profile type: Publication
full work available at URL: 0304-4149(87)90195-5
OpenAlex ID: W2023644181
cites work: On the growth of one dimensional contact processes
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cites work: Q5185817
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cites work: A dynamical phase transition in an infinite particle system
description: scientific article; zbMATH DE number 4018083