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A Note on Branching Random Walks on Finite Sets
Published online by Cambridge University Press: 14 July 2016
Abstract
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.
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- © Applied Probability Trust 2005
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