Quenched invariance principles for walks on clusters of percolation or among random conductances

被引：127
作者：
Sidoravicius, V
Sznitman, AS
机构：
[1] IMPA, BR-22460320 Rio De Janeiro, Brazil
[2] ETH Zentrum, Dept Math, CH-8092 Zurich, Switzerland
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2004年 / 129卷 / 02期
关键词：
D O I：
10.1007/s00440-004-0336-0
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：
In this work we principally study random walk on the supercritical infinite cluster for bond percolation on Z(d). We prove a quenched functional central limit theorem for the walk when dgreater than or equal to4. We also prove a similar result for random walk among i.i.d. random conductances along nearest neighbor edges of Z(d), when dgreater than or equal to1.
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页码：219 / 244
页数：26
相关论文
共 15 条
[1]   SYMMETRIC RANDOM-WALKS IN RANDOM-ENVIRONMENTS [J].
ANSHELEVICH, VV ;
KHANIN, KM ;
SINAI, YG .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 85 (03) :449-470
[2]   WEAK-CONVERGENCE FOR REVERSIBLE RANDOM-WALKS IN A RANDOM ENVIRONMENT [J].
BOIVIN, D .
ANNALS OF PROBABILITY, 1993, 21 (03) :1427-1440
[3]   Spectral homogenization of reversible random walks on Zd in a random environment [J].
Boivin, D ;
Depauw, J .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2003, 104 (01) :29-56
[4]  
Bolthausen Erwin, 2002, Methods Appl. Anal., V9, P345, DOI DOI 10.4310/MAA.2002.V9.N3.A4
[5]   Finite volume approximation of the effective diffusion matrix: The case of independent bond disorder [J].
Caputo, P ;
Ioffe, D .
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2003, 39 (03) :505-525
[6]  
Delmotte T, 1999, REV MAT IBEROAM, V15, P181
[7]   AN INVARIANCE-PRINCIPLE FOR REVERSIBLE MARKOV-PROCESSES - APPLICATIONS TO RANDOM MOTIONS IN RANDOM-ENVIRONMENTS [J].
DEMASI, A ;
FERRARI, PA ;
GOLDSTEIN, S ;
WICK, WD .
JOURNAL OF STATISTICAL PHYSICS, 1989, 55 (3-4) :787-855
[8]   Harnack inequalities and sub-Gaussian estimates for random walks [J].
Grigor'yan, A ;
Telcs, A .
MATHEMATISCHE ANNALEN, 2002, 324 (03) :521-556
[9]   RANDOM-WALK ON THE INFINITE CLUSTER OF THE PERCOLATION MODEL [J].
GRIMMETT, GR ;
KESTEN, H ;
ZHANG, Y .
PROBABILITY THEORY AND RELATED FIELDS, 1993, 96 (01) :33-44
[10]  
HELLAND IS, 1982, SCAND J STAT, V9, P79
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