Chase-escape with death on trees

TL;DR

This paper studies a variant of the chase-escape process on infinite trees where red particles can die, revealing a phase diagram and connecting critical behavior to weighted Catalan numbers.

Contribution

It introduces a new death variant of chase-escape and characterizes its phase diagram using a novel connection to weighted Catalan numbers.

Findings

Characterization of the phase diagram for the process

Identification of critical behavior via Catalan numbers

New insights into death dynamics in chase-escape models

Abstract

Chase-escape is a competitive growth process in which red particles spread to adjacent uncolored sites, while blue particles overtake adjacent red particles. We introduce the variant in which red particles die and describe the phase diagram for the resulting process on infinite d-ary trees. A novel connection to weighted Catalan numbers makes it possible to characterize the critical behavior.