Recent results on branching random walks

Daniela Bertacchi; Fabio Zucca

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arXiv · 1104.5085

Recent results on branching random walks

Daniela Bertacchi·Fabio Zucca

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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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Daniela Bertacchi, Fabio Zucca. 2011-04-27. Recent results on branching random walks. https://arxiv.org/abs/1104.5085

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