THE GENEALOGY OF BRANCHING BROWNIAN MOTION WITH ABSORPTION
THE GENEALOGY OF BRANCHING BROWNIAN MOTION WITH ABSORPTION
复制标题
DOI：
10.1214/11-aop728
复制
发表时间：
2013-03-01
影响因子：
2.3
通讯作者：
Schweinsberg, Jason
中科院分区：
文献类型：
--
作者：
Berestycki, Julien;Berestycki, Nathanael;Schweinsberg, Jason
我们考虑一个系统的粒子进行分支布朗运动负漂移和被杀死后达到零，在近临界状态下，总人口保持大致恒定的约N个粒子。我们表明，这个人口的演变的特征时间尺度是（log N）（3）的顺序，在这个意义上说，当时间在这些单位测量，缩放粒子数收敛到一个变量的Neveu的连续状态分支过程。此外，颗粒的谱系然后由被称为Bolthausen-Sznitman聚结剂的聚结过程控制。这验证了Brunet，Derrida，Muller和Munier对一个密切相关的模型的非严格预测。
We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total population stays roughly constant with approximately N particles. We show that the characteristic time scale for the evolution of this population is of order (log N)(3), in the sense that when time is measured in these units, the scaled number of particles converges to a variant of Neveu's continuous-state branching process. Furthermore, the genealogy of the particles is then governed by a coalescent process known as the Bolthausen-Sznitman coalescent. This validates the nonrigorous predictions by Brunet, Derrida, Muller and Munier for a closely related model.