Recurrence and transience of random walks in random environments on a strip

被引：42
作者：
Bolthausen, E
Goldsheid, I
机构：
[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland
[2] Univ London Queen Mary & Westfield Coll, Sch Math Sci, London E1 4NS, England
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2000年 / 214卷 / 02期
关键词：
D O I：
10.1007/s002200000279
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We explain the necessary and sufficient conditions for recurrent and transient behavior of a random walk in a stationary ergodic random environment on a strip in terms of properties of a top Lyapunov exponent. This Lyapunov exponent is defined for a product of a stationary sequence of positive matrices. In the one-dimensional case this approach allows us to treat wider classes of random walks than before.
引用
收藏
页码：429 / 447
页数：19
相关论文
共 14 条
[1]   A ZERO OR ONE LAW FOR ONE DIMENSIONAL RANDOM-WALKS IN RANDOM-ENVIRONMENTS [J].
ANDJEL, ED .
ANNALS OF PROBABILITY, 1988, 16 (02) :722-729
[2]  
[Anonymous], USPEKHI MAT NAUK
[3]   SHIFT-COUPLING AND A ZERO-ONE LAW FOR RANDOM-WALK IN RANDOM ENVIRONMENT [J].
DENHOLLANDER, F ;
THORISSON, H .
ACTA APPLICANDAE MATHEMATICAE, 1994, 34 (1-2) :37-50
[4]   PRODUCTS OF RANDOM MATRICES [J].
FURSTENBERG, H ;
KESTEN, H .
ANNALS OF MATHEMATICAL STATISTICS, 1960, 31 (02) :457-469
[5]   LOCALIZATION OF RANDOM-WALKS IN ONE-DIMENSIONAL RANDOM-ENVIRONMENTS [J].
GOLOSOV, AO .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1984, 92 (04) :491-506
[6]  
GREVEN A, 1994, ANN PROBAB, V22, P1267
[7]   GENERALIZED RANDOM-WALK IN A RANDOM ENVIRONMENT [J].
KALIKOW, SA .
ANNALS OF PROBABILITY, 1981, 9 (05) :753-768
[8]   THE LIMIT DISTRIBUTION OF SINAI RANDOM-WALK IN RANDOM ENVIRONMENT [J].
KESTEN, H .
PHYSICA A, 1986, 138 (1-2) :299-309
[9]  
KESTEN H, 1975, COMPOS MATH, V30, P145
[10]   RECURRENCE AND TRANSIENCE CRITERIA FOR RANDOM-WALK IN A RANDOM ENVIRONMENT [J].
KEY, ES .
ANNALS OF PROBABILITY, 1984, 12 (02) :529-560
12