Speed and fluctuations of N-particle branching Brownian motion with spatial selection

• 成果类型: Article
• 署名作者: Maillard, Pascal
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0701-9
• 发表日期: 2016
• 页码: 1061-1173
• 关键词: survival probability; equation; front; approximation; genealogy; BEHAVIOR; systems; times

摘要

We consider branching Brownian motion on the real line with the following selection mechanism: every time the number of particles exceeds a (large) given number N, only the N right-most particles are kept and the others killed. After rescaling time by , we show that the properly recentred position of the -th particle from the right, , converges in law to an explicitly given spectrally positive L,vy process. This behaviour has been predicted to hold for a large class of models falling into the universality class of the FKPP equation with weak multiplicative noise [Brunet et al. in Phys Rev E 73(5):056126 2006] and is proven here for the first time for such a model.