Weak quenched limit theorems for a random walk in a sparse random environment

被引：0

作者：

Buraczewski, Dariusz ^{[1
]}

Dyszewski, Piotr ^{[1
]}

Kolodziejska, Alicja ^{[1
]}

机构：

[1] Univ Wroclaw, Math Inst, Pl Grunwaldzki 2, PL-50384 Wroclaw, Poland

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2024年 / 29卷

关键词：

weak convergence; point processes; regular variation; random walk in a random environment; sparse random environment; DIMENSIONAL RANDOM-WALK; TRANSIENT RANDOM-WALKS;

D O I：

10.1214/23-EJP1070

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 study the quenched behaviour of a perturbed version of the simple symmetric random walk on the set of integers. The random walker moves symmetrically with an exception of some randomly chosen sites where we impose a random drift. We show that if the gaps between the marked sites are i.i.d. and regularly varying with a sufficiently small index, then there is no strong quenched limit laws for the position of the random walker. As a consequence we study the quenched limit laws in the context of weak convergence of random measures.

引用

页数：30

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