MINIMAL POSITIONS IN A BRANCHING RANDOM WALK
成果类型：
Article
署名作者：
McDiarmid, Colin
署名单位：
University of Oxford
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004832
发表日期：
1995
页码：
128-139
关键词：
摘要：
We consider a branching random walk on the real line, with mean family size greater than 1. Let B-n denote the minimal position of a member of the nth generation. It is known that (under a weak condition) there is a finite constant gamma, defined in terms of the distributions specifying the process, such that as n -> infinity, we have B-n = gamma n + o(n) a.s. on the event S of ultimate survival. Our results here show that (under appropriate conditions), on S the random variable B-n is strongly concentrated and the o(n) error term may be replaced by O(log n).