EXCITED RANDOM WALK

被引：75

作者：

Benjamini, Itai ^{[1
]}

Wilson, David B. ^{[2
]}

机构：

[1] Weizmann Inst Sci, IL-76100 Rehovot, Israel

[2] Microsoft Res, One Microsoft Way, Redmond, WA 98052 USA

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2003年 / 8卷

关键词：

Perturbed random walk; transience;

D O I：

10.1214/ECP.v8-1072

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：

A random walk on Z(d) is excited if the first time it visits a vertex there is a bias in one direction, but on subsequent visits to that vertex the walker picks a neighbor uniformly at random. We show that excited random walk on Z(d) is transient iff d > 1.

引用

页码：86 / 92

页数：7

共 16 条

[1] RANDOM WALKS THAT AVOID THEIR PAST CONVEX HULL
Angel, Omer
Benjamini, Itai
Virag, Balint
[J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2003, 8 : 6 - 16
[2] Bass RF, 2002, ANN PROBAB, V30, P1369
[3] Walks on the slit plane
Bousquet-Mélou, M
Schaeffer, G
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2002, 124 (03) : 305 - 344
[4] Davis B, 1996, ANN PROBAB, V24, P2007
[5] Brownian motion and random walk perturbed at extrema
Davis, B
[J]. PROBABILITY THEORY AND RELATED FIELDS, 1999, 113 (04) : 501 - 518
[6] Davis Burgess, 1990, THEORY RELAT FIELDS, V84, P203
[7] Doyle P. G., 1984, ARXIVMATHPR0001057 M
[8] Durrett R, 1996, PROBABILITY THEORY E
[9] DVORETZKY A, 1951, P 2 BERK S MATH STAT, P353
[10] EXTENDED WATSON INTEGRALS FOR CUBIC LATTICES
GLASSER, ML
ZUCKER, IJ
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1977, 74 (05) : 1800 - 1801

← 1 2 →