Stationary distribution for dioecious branching particle systems with rapid stirring

TL;DR

This paper investigates the stationary distributions of dioecious branching particle systems with two types of particles, demonstrating nontrivial distributions under conditions like rapid stirring, which models the interaction of male and female populations.

Contribution

It provides new insights into the conditions for nontrivial stationary distributions in two-sex branching particle systems, especially highlighting the role of rapid stirring.

Findings

Stationary distributions are nontrivial under certain conditions.

Rapid stirring influences the existence of stationary distributions.

The model captures dynamics of two-sex populations with interaction.

Abstract

We study dioecious (i.e., two-sex) branching particle system models, where there are two types of particles, modeling the male and female populations, and where birth of new particles requires the presence of both male and female particles. We show that stationary distributions of various dioecious branching particle models are nontrivial under certain conditions, for example, when there is sufficiently fast stirring.