On the limiting velocity of random walks in mixing random environment

被引：2
作者：
Guo, Xiaoqin
机构：
[1] 85748 Garching
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2014年 / 50卷 / 02期
关键词：
Random walks; Random environment; Mixing; Limiting speed; Conditional law of large numbers; ZERO-ONE LAW; LARGE NUMBERS;
D O I：
10.1214/12-AIHP534
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 consider random walks in strong-mixing random Gibbsian environments in Z(d),d >= 2. Based on regeneration arguments, we will first provide an alternative proof of Rassoul-Agha's conditional law of large numbers (CLLN) for mixing environment (Electron. Commun. Probab. 10 (2005) 36-44). Then, using coupling techniques, we show that there is at most one nonzero limiting velocity in high dimensions (d >= 5).
引用
收藏
页码：375 / 402
页数：28
相关论文
共 14 条
[1]  
[Anonymous], 1837, LECT PROBABILITY THE
[2]  
[Anonymous], PROGR PHYS
[3]   Limiting velocity of high-dimensional random walk in random environment [J].
Berger, Noam .
ANNALS OF PROBABILITY, 2008, 36 (02) :728-738
[4]   Gaussian fluctuations for random walks in random mixing environments [J].
Comets, F .
ISRAEL JOURNAL OF MATHEMATICS, 2005, 148 (1) :87-113
[5]  
Comets F, 2004, ANN PROBAB, V32, P880
[6]   Limit velocity and zero-one laws for diffusions in random environment [J].
Goergen, Laurent .
ANNALS OF APPLIED PROBABILITY, 2006, 16 (03) :1086-1123
[7]   On the zero-one law and the law of large numbers for random walk in mixing random environment [J].
Rassoul-Agha, F .
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2005, 10 :36-44
[8]   Large deviations for random walks in a mixing random environment and other (non-Markov) random walks [J].
Rassoul-Agha, F .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (09) :1178-1196
[9]   The point of view of the particle on the law of large numbers for random walks in a mixing random environment [J].
Rassoul-Agha, F .
ANNALS OF PROBABILITY, 2003, 31 (03) :1441-1463
[10]   RANDOM-WALKS IN A RANDOM ENVIRONMENT [J].
SOLOMON, F .
ANNALS OF PROBABILITY, 1975, 3 (01) :1-31
12