Extinction probability and total progeny of predator-prey dynamics on infinite trees. (English) Zbl 1307.60115

Bordenave, Charles

Electron. J. Probab. 19, Paper No. 20, 33 p. (2014).

Author’s 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 G. Kordzakhia [Electron. Commun. Probab. 10, 113–124 (2005; Zbl 1111.60075)] and it admits a limit process, the birth-and-assassination process, previously introduced by D. Aldous and W. B. Krebs [Stat. Probab. Lett. 10, No. 5, 427–430 (1990; Zbl 0712.60090)]. 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.

Reviewer: Aleksander Iksanov (Kiev)

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60J85	Applications of branching processes
92D25	Population dynamics (general)

Keywords:

branching processes; infinite trees; predator-prey dynamics; SIR models

Citations:

Zbl 1111.60075; Zbl 0712.60090