Weak Quenched Invariance Principle for Random Walk with Random Environment in Time

被引：0

作者：

Lu, You ^{[1
]}

Hong, Wenming ^{[2
,3
]}

机构：

[1] Donghua Univ, Sch Math & Stat, Shanghai 201620, Peoples R China

[2] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[3] Beijing Normal Univ, Key Lab Math & Complex Syst, Beijing 100875, Peoples R China

来源：

FRONTIERS OF MATHEMATICS | 2025年

基金：

中国国家自然科学基金;

关键词：

Random environment; invariance principle; weak quenched limits; BRANCHING RANDOM-WALKS; APPROXIMATION; PERCOLATION; SURVIVAL; KOMLOS;

D O I：

10.1007/s11464-022-0348-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the invariance principle for a random walk with a random environment (denoted by mu) in time on & Ropf; in a weak quenched sense. We show that a sequence of random probability measures on & Ropf; generated by mu and a bounded Lipschitz functional f will converge in distribution to another random probability measure, which can be represented by f and two independent Brownian motions. The upper bound of the convergence rate has been obtained. We also explain that in general, this convergence can not be strengthened to the almost surely sense.

引用

页数：15

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