Recent results on branching random walks

2011/04/27 by Daniela Bertacchi, Bertacchi, Daniela, Fabio Zucca +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #60J80 #60K35 #Diffusion and Search Dynamics #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1104.5085

openalex publication_date 2011/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the existence of a pure global survival phase and the approximation of branching random walks by means of multitype contact processes or spatially confined branching random walks. Most results are obtained using a generating function approach: the probabilities of extinction are seen as fixed points of an infinite dimensional power series. Throughout this paper we provide many nontrivial examples and counterexamples.

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