Approximating critical parameters of branching random walks
Daniela Bertacchi and Fabio Zucca
Source: J. Appl. Probab. Volume 46, Number 2 (2009), 463-478.
Abstract
Given a branching random walk on a graph, we consider two kinds of truncations: either by inhibiting the reproduction outside a subset of vertices or by allowing at most $m$ particles per vertex. We investigate the convergence of weak and strong critical parameters of these truncated branching random walks to the analogous parameters of the original branching random walk. As a corollary, we apply our results to the study of the strong critical parameter of a branching random walk restricted to the cluster of a Bernoulli bond percolation.
Primary Subjects: 60K35
Keywords: Branching random walk; critical parameters; percolation; graphs
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1245676100
Digital Object Identifier: doi:10.1239/jap/1245676100
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05578819
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MR2535826
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