Approximating critical parameters of branching random walks

Details Approximating critical parameters of branching random walks Approximating critical parameters of branching random walks

2007-10-19

arxiv.org/abs/0710.3792v3

J.Appl.Probab., 46 (2009), 463-478

Mathematics

Probability

15 pages, 4 figures. Added missing acknowledgments

Scientific paper

Given a branching random walk on a graph, we consider two kinds of truncations: by inhibiting the reproduction outside a subset of vertices and by allowing at most $m$ particles per site. 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.

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