A note on branching random walks on finite sets
Thomas Mountford and Rinaldo B. Schinazi
Source: J. Appl. Probab. Volume 42, Number 1
(2005), 287-294.
Abstract
We show that a branching random walk that is supercritical on Zd is also supercritical, in a rather strong sense, when restricted to a large enough finite ball of Zd. This implies that the critical value of branching random walks on finite balls converges to the critical value of branching random walks on Zd as the radius increases to infinity. Our main result also implies coexistence of an arbitrary finite number of species for an ecological model.
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Keywords: Branching random walk; coexistence; ecological model; spatial stochastic model; contact process
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1110381389
Digital Object Identifier: doi:10.1239/jap/1110381389
Mathematical Reviews number (MathSciNet): MR2144912
Zentralblatt MATH identifier: 1074.60102
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Journal of Applied Probability
