POISSON-DIRICHLET BRANCHING RANDOM WALKS

被引：9

作者：

Addario-Berry, Louigi ^{[1
]}

Ford, Kevin ^{[2
]}

机构：

[1] McGill Univ, Montreal, PQ H3A 2K6, Canada

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

ANNALS OF APPLIED PROBABILITY | 2013年 / 23卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Branching random walk; random recursive tree; Pratt tree; heights of trees; ARY SEARCH-TREES; MINIMAL POSITION; WEAK-CONVERGENCE; HEIGHTS;

D O I：

10.1214/12-AAP840

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 determine, to within 0(1), the expected minimal position at level n in certain branching random walks. The walks under consideration have displacement vector (nu 1, nu 2, ... ), where each vi is the sum of j independent Exponential(1) random variables and the different vi need not be independent. In particular, our analysis applies to the Poisson-Dirichlet branching random walk and to the Poisson-weighted infinite tree. As a corollary, we also determine the expected height of a random recursive tree to within O(1).

引用

页码：283 / 307

页数：25

共 23 条

[1] MINIMA IN BRANCHING RANDOM WALKS [J].