English

Barycentric Brownian Bees

Probability 2021-08-17 v2

Abstract

We establish an invariance principle for the barycenter of a Brunet-Derrida particle system in dd dimensions. The model consists of NN particles undergoing dyadic branching Brownian motion with rate 11. At a branching event, the number of particles is kept equal to NN 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

R2 v1 2026-06-23T16:09:12.887Z