This chapter 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 chapter we provide many nontrivial examples and counterexamples.
Bertacchi, D., Zucca, F. (2013). Recent results on branching random walks. In A. Skogseid, V. Fasano (a cura di), Statistical Mechanics and Random Walks: Principles, Processes and Applications (pp. 289-340). Nova Science Publishers.
Recent results on branching random walks
BERTACCHI, DANIELA;
2013
Abstract
This chapter 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 chapter we provide many nontrivial examples and counterexamples.
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