SUB-GAUSSIAN TAIL BOUNDS FOR THE WIDTH AND HEIGHT OF CONDITIONED GALTON-WATSON TREES

被引：38
作者：
Addario-Berry, Louigi [1 ]
Devroye, Luc [2 ]
Janson, Svante [3 ]
机构：
[1] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada
[2] McGill Univ, Sch Comp Sci, Montreal, PQ H3A 2A7, Canada
[3] Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden
来源：
ANNALS OF PROBABILITY | 2013年 / 41卷 / 02期
关键词：
Random trees; Galton-Watson trees; simply generated trees; width; height; BEHAVIOR;
D O I：
10.1214/12-AOP758
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：
We study the height and width of a Galton-Watson tree with offspring distribution xi satisfying E xi = 1, 0 < Var xi < infinity, conditioned on having exactly n nodes. Under this conditioning, we derive sub-Gaussian tail bounds for both the width (largest number of nodes in any level) and height (greatest level containing a node); the bounds are optimal up to constant factors in the exponent. Under the same conditioning, we also derive essentially optimal upper tail bounds for the number of nodes at level k, for 1 <= k <= n.
引用
收藏
页码：1072 / 1087
页数：16
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