Are there bushes in a forest?
type: Item
instance of: scholarly article
title: Are there bushes in a forest?
zbMATH Open document ID: 0722.60106
DOI: 10.1016/0304-4149(91)90057-J
published in: Stochastic Processes and their Applications
publication date: 1991-01-01T00:00:00Z
review text: The authors study a Markov process, whose state space consists of the configurations on \({\mathbb{Z}}^ d\), where each site is in one of the three states 0, 1 and 2 resp. grass, bush, tree. They assume, that 1's and 2's die (i.e. become 0) at rate 1 and produce offsprings at rate \(\lambda_ 1\) resp. \(\lambda_ 2\), which replace the state at a position of a certain neighbourhood with equal probability, if this site is in a lower state. Sufficient conditions are given both for the case, that 1's die out as for the case of permanent coexistence of 1's and 2's.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 4190892
zbMATH Keywords: interacting particle systems
zbMATH Keywords: birth-and-death processes
author: Rick Durrett
author: G. H. Swindle
MaRDI profile type: Publication
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full work available at URL: 0304-4149(91)90057-j
OpenAlex ID: W2034765212
description: scientific article; zbMATH DE number 4190892