MINIMA IN BRANCHING RANDOM WALKS

被引：87
|
作者：
Addario-Berry, Louigi [1 ]
Reed, Bruce [2 ,3 ]
机构：
[1] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada
[2] McGill Univ, Sch Comp Sci, Canada Res Chair, Montreal, PQ H3A 2A7, Canada
[3] INRIA, Equipe Mascotte, Labo 13S, Sophia Antipolis, France
来源：
ANNALS OF PROBABILITY | 2009年 / 37卷 / 03期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Branching random walks; branching processes; random trees; WEIGHTED HEIGHT; DISPLACEMENT; DEVIATIONS; POSITION;
D O I：
10.1214/08-AOP428
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Given a branching random walk, let M-n be the minimum position of any member of the nth generation. We calculate EMn to within O(1) and prove exponential tail bounds for P{vertical bar M-n - EMn vertical bar > x}, under quite general conditions on the branching random walk. In particular, together with work by Bramson [Z. Wahrsch. Verw. Gebiete 45 (1978) 89-108], our results fully characterize the possible behavior of EMn when the branching random walk has bounded branching and step size.
引用
收藏
页码：1044 / 1079
页数：36
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