On the maximal displacement of critical branching random walk
成果类型：
Article
署名作者：
Lalley, Steven P.; Shao, Yuan
署名单位：
University of Chicago; University of Chicago
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-014-0566-8
发表日期：
2015
页码：
71-96
关键词：
摘要：
We consider a branching random walk initiated by a single particle at location in which particles alternately reproduce according to the law of a Galton-Watson process and disperse according to the law of a driftless random walk on the integers. When the offspring distribution has mean the branching process is critical, and therefore dies out with probability . We prove that if the particle jump distribution has mean zero, positive finite variance , and finite moment, and if the offspring distribution has positive variance and finite third moment then the distribution of the rightmost position reached by a particle of the branching random walk satisfies as . We also prove a conditional limit theorem for the distribution of the rightmost particle location at time given that the process survives for generations.