Branching random walks and contact processes on Galton-Watson trees. (English) Zbl 1291.60177

Su, Wei

Electron. J. Probab. 19, Paper No. 41, 12 p. (2014).

Summary: We consider branching random walks and contact processes on infinite, connected, locally finite graphs whose reproduction and infectivity rates across edges are inversely proportional to vertex degree. We show that when the ambient graph is a Galton-Watson tree then, in certain circumstances, the branching random walks and contact processes will have weak survival phases. We also provide bounds on critical values.

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60J99	Markov processes

Keywords:

branching random walk; contact process; Galton-Watson tree; phase transition