Weak survival for branching random walks on graphs

Details Weak survival for branching random walks on graphs Weak survival for branching random walks on graphs

2006-03-16

arxiv.org/abs/math/0603412v2

J.Appl.Prob. 45 n.2 (2008), 481-497

Mathematics

Probability

20 pages; corrected typos and weakened Definition 3.6

Scientific paper

We study weak and strong survival for branching random walks on multigraphs.
We prove that, for a large class of multigraphs, weak survival is related to a
geometrical parameter of the multigraph and that the existence of a pure weak
phase is equivalent to nonamenability. Finally we study weak and strong
critical behaviors of the branching random walk.

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