Extinction probability and total progeny of predator-prey dynamics on infinite trees

TL;DR

This paper analyzes the extinction probability and total progeny in predator-prey dynamics on infinite trees, focusing on the chase-escape model and its limit process, providing asymptotic and tail bounds near criticality.

Contribution

It offers new asymptotic estimates for extinction probabilities and tail bounds for total progeny in the chase-escape model on infinite trees.

Findings

Asymptotic equivalent of extinction probability near criticality

Tail bounds on total progeny in the subcritical regime

Analysis of the birth-and-assassination process as a limit model

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.