Barycentric Brownian Bees
Probability
2021-08-17 v2
Abstract
We establish an invariance principle for the barycenter of a Brunet-Derrida particle system in dimensions. The model consists of particles undergoing dyadic branching Brownian motion with rate . At a branching event, the number of particles is kept equal to by removing the particle located furthest away from the barycenter. To prove the invariance principle, a key step is to establish Harris recurrence for the process viewed from its barycenter.
Keywords
Cite
@article{arxiv.2006.04743,
title = {Barycentric Brownian Bees},
author = {Louigi Addario-Berry and Jessica Lin and Thomas Tendron},
journal= {arXiv preprint arXiv:2006.04743},
year = {2021}
}
Comments
36 pages. This version incorporates useful feedback from an anonymous referee. To appear in Annals of Applied Probability