Abstract
We establish an invariance principle for the barycenter of a Brunet–Derrida particle system in d dimensions. The model consists of N particles undergoing dyadic branching Brownian motion with rate 1. At a branching event, the number of particles is kept equal to N 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.
Funding Statement
LAB was partially supported by NSERC Discovery Grant 643473 and Discovery Accelerator Supplement 643474, and FRQNT Grant 206470.
JL was partially supported by NSERC Discovery Grant 247764, FRQNT Grant 250479, and the Canada Research Chairs program. TT was partially supported by FRQNT Grant 250479.
Acknowledgements
The authors would all like to thank Julien Berestycki and Sarah Penington for helpful discussions and correspondence, in particular regarding their related work; and to thank Jeremy Quastel for initially proposing the study of this model in 2012. The authors would also like to thank an anonymous referee for an extremely careful reading that substantially improved the paper.
Citation
Louigi Addario-Berry. Jessica Lin. Thomas Tendron. "Barycentric Brownian bees." Ann. Appl. Probab. 32 (4) 2504 - 2539, August 2022. https://doi.org/10.1214/21-AAP1738
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