Stationary distribution for dioecious branching particle systems with rapid stirring

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.Comment: Published in at http://dx.doi.org/10.1214/105051607000000276 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org