Recent results on branching random walks

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.

52 pages, 4 figures, added a new property on the probability of never visiting a subset for a BRW

References in corpus (2)

• Characterization of the critical values of branching random walks on weighted graphs through infinite-type branching processes
• Survival, extinction and approximation of discrete-time branching random walks

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