Dimensions of random trees

被引：4
|
作者：
Konsowa, MH
Oraby, TF
机构：
[1] Helwan Univ, Fac Sci, Dept Math, Cairo, Egypt
[2] Cairo Univ, Fac Sci, Dept Math, Cairo, Egypt
来源：
STATISTICS & PROBABILITY LETTERS | 2003年 / 62卷 / 01期
关键词：
random trees; Galton-Waston tree; random walks;
D O I：
10.1016/S0167-7152(02)00424-8
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：
In this paper we show, for Galton-Watson tree T of resistance R, that R - R-n decays exponentially in n where R-n denotes the resistance of the portion of T between the root and level n. We also determine a formula for the resistance dimension of spherically symmetric random trees and prove that it is equal to the fractal dimension. We emphasize the relationship between these dimensions and the type, of being transient or recurrent, of the simple random walks on such trees. (C) 2003 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：49 / 60
页数：12
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