The contact process on a finite set. II
type: Item
instance of: scholarly article
title: The contact process on a finite set. II
zbMATH Open document ID: 0664.60106
author: Roberto H. Schonmann
author: Rick Durrett
published in: The Annals of Probability
publication date: 1988-01-01T00:00:00Z
review text: In this paper we complete the work started in part I by the first author and \textit{X.-F. Liu} [ibid., No.3, 1158-1173 (1988; Zbl 0647.60105)]. We show that if \(\sigma_ N\) is the time that the contact process on \(\{\) 1,...,N\(\}\) first hits the empty set, then for \(\lambda >\lambda_ c\) (the critical value for the process on Z) there is a positive constant \(\gamma\) (\(\lambda)\) so that (log \(\sigma_ N)/N\to \gamma (\lambda)\) in probability as \(N\to \infty\). We also give a new simple proof that \(\sigma_ N/E \sigma_ N\) converges to a mean one exponential. The keys to the proof of the first result are a ``planar graph duality'' for the contact process and an observation of J. Chayes and L. Chayes that exponential decay rates for connections in strips approach the decay rates in the plane as the width of the strip goes to \(\infty\).
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4086722
zbMATH Keywords: biased voter model
zbMATH Keywords: contact process
zbMATH Keywords: planar graph duality
Wikidata QID: Q98839746
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991584
OpenAlex ID: W2014945524
DOI: 10.1214/AOP/1176991584
description: scientific article; zbMATH DE number 4086722