EXTENDED CONVERGENCE OF THE EXTREMAL PROCESS OF BRANCHING BROWNIAN MOTION

• 成果类型: Article
• 署名作者: Bovier, Anton; Hartung, Lisa
• 署名单位: University of Bonn; New York University; University of Bonn
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1244
• 发表日期: 2017
• 页码: 1756-1777
• 关键词: GAUSSIAN MULTIPLICATIVE CHAOS

摘要

We extend the results of Arguin et al. [Probab. Theory Related Fields 157 (2013) 535-574] and Aidekon et al. [Probab. Theory Related Fields 157 (2013) 405-451] on the convergence of the extremal process of branching Brownian motion by adding an extra dimension that encodes the location of the particle in the underlying Galton-Watson tree. We show that the limit is a cluster point process on R+ x R where each cluster is the atom of a Poisson point process on R+ x R with a random intensity measure Z (dz) x Ce-root 2x dx, where the random measure is explicitly constructed from the derivative martingale. This work is motivated by an analogous result for the Gaussian free field by Biskup and Louidor [Full extremal process, cluster law and freezing for two-dimensional discrete Gaussian free field (2016)].