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Approximating Critical Parameters of Branching Random Walks

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Daniela Bertacchi  and
Fabio Zucca
Daniela Bertacchi*
Affiliation:
Università di Milano–Bicocca
Fabio Zucca*
Affiliation:
Politecnico di Milano
*
∗Postal address: Dipartimento di Matematica e Applicazioni, Università di Milano–Bicocca, Via Cozzi 53, 20125 Milano, Italy. Email address: daniela.bertacchi@unimib.it
∗∗Postal address: Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy. Email address: fabio.zucca@polimi.it
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Abstract

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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.

Keywords

Branching random walkcritical parameterspercolationgraphs

MSC classification

Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 463 - 478
Copyright
Copyright © Applied Probability Trust 2009 

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