Weak survival for branching random walks on graphs

Abstract

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.

20 pages; corrected typos and weakened Definition 3.6

Cited by in corpus (2)

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