Coalescence times for critical Galton-Watson processes with immigration

Rong-Li Liu; Yan-Xia Ren; Yingrui Wang

paper

Coalescence times for critical Galton-Watson processes with immigration

arXiv:2307.07384

Abstract

Let $X_{n}^{I}$ be the coalescence time of two particles picked at random from the $n$ th generation of a critical Galton-Watson process with immigration, and let $A_{n}^{I}$ be the coalescence time of the whole population in the $n$ th generation. In this paper, we study the limiting behaviors of $X_{n}^{I}$ and $A_{n}^{I}$ as $n \to \infty$ .