Systems of branching, annihilating, and coalescing particles

TL;DR

This paper analyzes particle systems with branching, coalescence, and annihilation, showing that adding annihilation doesn't significantly alter long-term behavior and can be modeled as thinned versions of systems without annihilation.

Contribution

It extends previous work by incorporating annihilation into particle systems, demonstrating that these systems can be understood through thinning of non-annihilating systems.

Findings

Adding annihilation does not significantly change long-time behavior.

Systems with annihilation can be obtained by thinning systems without annihilation.

The non-monotonicity and duality complexities are addressed.

Abstract

This paper studies systems of particles following independent random walks and subject to annihilation, binary branching, coalescence, and deaths. In the case without annihilation, such systems have been studied in our 2005 paper "Branching-coalescing particle systems". The case with annihilation is considerably more difficult, mainly as a consequence of the non-monotonicity of such systems and a more complicated duality. Nevertheless, we show that adding annihilation does not significantly change the long-time behavior of the process and in fact, systems with annihilation can be obtained by thinning systems without annihilation.