Branching capacity of a random walk in Z5

被引：0

作者：

Bai, Tianyi ^{[1
]}

Delmas, Jean-Francois ^{[2
]}

Hu, Yueyun ^{[3
]}

机构：

[1] Chinese Acad Sci, AMSS, Beijing, Peoples R China

[2] Ecole Ponts, CERMICS, Marne, France

[3] Univ Paris XIII, LAGA, Paris, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2025年 / 30卷

关键词：

branching capacity; range; random walk; critical branching random walk; INTERSECTION-PROPERTIES; ALEATORY WALKS; RANGE; CONVERGENCE;

D O I：

10.1214/25-EJP1334

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 are interested in the branching capacity of the range of a random walk in Zd. Schapira [29] has recently obtained precise asymptotics in the case d >= 6 and has demonstrated a transition at dimension d = 6. We study the case d = 5 and prove that the renormalized branching capacity converges in law to the Brownian snake capacity of the range of a Brownian motion. The main step in the proof relies on studying the intersection probability between the range of a critical Branching random walk and that of a random walk, which is of independent interest.

引用

页数：26

共 33 条

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