Extinction probability and total progeny of predator-prey dynamics on infinite trees
Abstract
We consider the spreading dynamics of two nested invasion clusters on an infinite tree. This model was defined as the chase-escape model by Kordzakhia and it admits a limit process, the birth-and-assassination process, previously introduced by Aldous and Krebs. On both models, we prove an asymptotic equivalent of the extinction probability near criticality. In the subcritical regime, we give a tail bound on the total progeny of the preys before extinction.
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Pages: 1-33
Publication Date: February 7, 2014
DOI: 10.1214/EJP.v19-2361
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