Existence of the Harmonic Measure for Random Walks on Graphs and in Random Environments

被引：4

作者：

Boivin, Daniel ^{[1
]}

Rau, Clement ^{[2
]}

机构：

[1] Univ Bretagne Occidentale, Math Lab, CNRS, UMR 6205, F-29238 Brest, France

[2] Univ Toulouse 3, Inst Math Toulouse, F-31400 Toulouse, France

来源：

JOURNAL OF STATISTICAL PHYSICS | 2013年 / 150卷 / 02期

关键词：

Harmonic measure; Supercritical percolation clusters; Harnack inequality; Green kernel; Random conductance model; QUENCHED INVARIANCE-PRINCIPLES; PARABOLIC HARNACK INEQUALITY; PERCOLATION CLUSTERS; UNBOUNDED CONDUCTANCES; POTENTIAL-THEORY; FRACTALS; MODEL;

D O I：

10.1007/s10955-012-0685-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on a"currency sign (d) , da parts per thousand yen3, when the conductances are i.i.d. and the bonds with positive conductance percolate. The harmonic measure from infinity also exists for random walks on supercritical clusters of a"currency sign(2). This is proved using results of Barlow (Ann. Probab. 32:3024-3084, 2004) and Barlow and Hambly (Electron. J. Probab. 14(1):1-27, 2009).

引用

页码：235 / 263

页数：29

共 38 条

[1] The harmonic measure of diffusion-limited aggregates including rare events [J].

Adams, D. A. ;

Sander, L. M. ;

Somfai, E. ;

Ziff, R. M. .

EPL, 2009, 87 (02)

[2] Harmonic measure for percolation and Ising clusters including rare events [J].

Adams, David A. ;

Sander, Leonard M. ;

Ziff, Robert M. .

PHYSICAL REVIEW LETTERS, 2008, 101 (14)

[3] Invariance principle for the random conductance model [J].

Andres, S. ;

Barlow, M. T. ;

Deuschel, J. -D. ;

Hambly, B. M. .

PROBABILITY THEORY AND RELATED FIELDS, 2013, 156 (3-4) :535-580

[4]

[Anonymous], 2009, American Mathematical Soc.

[5]

[Anonymous], 1976, Principles of Random Walk

[6]

[Anonymous], 2010, CAMBRIDGE STUDIES AD

[7]

[Anonymous], 2006, LECT NOTES MATH

[8]

Antal P, 1996, ANN PROBAB, V24, P1036

[9] INVARIANCE PRINCIPLE FOR THE RANDOM CONDUCTANCE MODEL WITH UNBOUNDED CONDUCTANCES [J].

Barlow, M. T. ;

Deuschel, J-D. .

ANNALS OF PROBABILITY, 2010, 38 (01) :234-276

[10]

Barlow MT, 2009, ELECTRON J PROBAB, V14

← 1 2 3 4 →