BARYCENTRIC BROWNIAN BEES

• 成果类型: Article
• 署名作者: Addario-Berry, Louigi; Lin, Jessica; Tendron, Thomas
• 署名单位: McGill University; University of Oxford
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1738
• 发表日期: 2022
• 页码: 2504-2539
• 关键词: particle-systems; selection

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.