Immortal Branching Processes
Abstract
We introduce and study the dynamics of an \emph{immortal} critical branching process. In the classic, critical branching process, particles give birth to a single offspring or die at the same rates. Even though the average population is constant in time, the ultimate fate of the population is extinction. We augment this branching process with immortality by positing that either: (a) a single particle cannot die, or (b) there exists an immortal stem cell that gives birth to ordinary cells that can subsequently undergo critical branching. We discuss the new dynamical aspects of this immortal branching process.
Cite
@article{arxiv.2101.04498,
title = {Immortal Branching Processes},
author = {P. L. Krapivsky and S. Redner},
journal= {arXiv preprint arXiv:2101.04498},
year = {2021}
}
Comments
12 pages. For the special edition of Physica A in memory of Dietrich Stauffer. Version 2 contains some additional material and a few other changes in response to referee comments