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A Note on Branching Random Walks on Finite Sets
- Part of
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- Journal:
- Journal of Applied Probability / Volume 42 / Issue 1 / March 2005
- Published online by Cambridge University Press:
- 14 July 2016, pp. 287-294
- Print publication:
- March 2005
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- Article
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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.
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.