BARYCENTRIC BROWNIAN BEES

Addario-Berry Louigi,Lin Jessica, Tendron Thomas

ANNALS OF APPLIED PROBABILITY（2022）

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摘要

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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关键词

Branching brownian motion, Brownian bees, Brunet-Derrida particle systems, invariance principle, Harris recurrence

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