Barycentric Brownian Bees

Louigi Addario-Berry; Jessica Lin; Thomas Tendron

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arXiv · 2006.04743

Barycentric Brownian Bees

Louigi Addario-Berry·Jessica Lin·Thomas Tendron

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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.

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Louigi Addario-Berry, Jessica Lin, Thomas Tendron. 2020-06-08. Barycentric Brownian Bees. https://arxiv.org/abs/2006.04743

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