MINIMA IN BRANCHING RANDOM WALKS

被引：90

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

页码：1044 / 1079

页数：36

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