On the critical branching random walk III: The critical dimension

被引：2

作者：

Zhu, Qingsan ^{[1
]}

机构：

[1] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2021年 / 57卷 / 01期

基金：

欧洲研究理事会;

关键词：

Critical branching random walk; Tree-indexed random walk; Visiting probability; Harmonic measure; Range; RANGE;

D O I：

10.1214/20-AIHP1071

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 study the critical branching random walk in the critical dimension, four. We provide the asymptotics of the probability of visiting a fixed finite set and the range of the critical branching random walk conditioned on the total number of offspring. We also prove that conditioned on visiting a finite set, the first visiting point converges in distribution, when the starting point tends to infinity.

引用

页码：73 / 93

页数：21

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