On the boundary at infinity for branching random walk

被引：0

作者：

Candellero, Elisabetta ^{[1
]}

Hutchcroft, Tom ^{[2
]}

机构：

[1] Roma Tre Univ, Dept Math & Phys, Rome, Italy

[2] CALTECH, Div Phys Math & Astron, Pasadena, CA 91125 USA

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2023年 / 28卷

关键词：

Martin boundary; branching random walk; Markov chains; POISSON FORMULA; LIMIT-THEOREM; TRANSITION; GRAPHS; NUMBER;

D O I：

10.1214/23-ECP560

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 prove that a supercritical branching random walk on a transient Markov chain converges almost surely under rescaling to a random measure on the Martin boundary of the underlying Markov chain. Several open problems and conjectures about this limiting measure are presented.

引用

页数：12

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