Frequent points for random walks in two dimensions

被引：0

作者：

Bass, Richard F. ^{[1
]}

Rosen, Jay

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] CUNY Coll Staten Isl, Dept Math, Staten Isl, NY 10314 USA

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2007年 / 12卷

关键词：

random walks; Green's functions; Harnack inequalities; frequent points;

D O I：

暂无

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：

For a symmetric random walk in Z(2) which does not necessarily have bounded jumps we study those points which are visited an unusually large number of times. We prove the analogue of the Erdos-Taylor conjecture and obtain the asymptotics for the number of visits to the most visited site. We also obtain the asymptotics for the number of points which are visited very frequently by time n. Among the tools we use are Harnack inequalities and Green's function estimates for random walks with unbounded jumps; some of these are of independent interest.

引用

页数：46

共 13 条

[1] LOCAL-TIMES ON CURVES AND UNIFORM INVARIANCE-PRINCIPLES [J].