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A Note on Branching Random Walks on Finite Sets

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Thomas Mountford  and
Rinaldo B. Schinazi
Thomas Mountford*
Affiliation:
EPFL-DMA
Rinaldo B. Schinazi*
Affiliation:
University of Colorado
*
∗ Postal address: EPFL-DMA, CH-1015 Lausanne, Switzerland. Email address: thomas.mountford@epfl.ch
∗∗ Postal address: Department of Mathematics, University of Colorado, Colorado Springs, CO 80933, USA. Email address: schinazi@math.uccs.edu
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Abstract

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We show that a branching random walk that is supercritical on is also supercritical, in a rather strong sense, when restricted to a large enough finite ball of This implies that the critical value of branching random walks on finite balls converges to the critical value of branching random walks on as the radius increases to infinity. Our main result also implies coexistence of an arbitrary finite number of species for an ecological model.

Keywords

Branching random walkcoexistenceecological modelspatial stochastic modelcontact process

MSC classification

Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 287 - 294
Copyright
© Applied Probability Trust 2005 

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