Daniela Bertacchi, Fabio Zucca
Published 2006-03-16, updated 2007-01-10Version 2
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.
Comments: 20 pages; corrected typos and weakened Definition 3.6
Journal: J.Appl.Prob. 45 n.2 (2008), 481-497
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