Ergodic theory on stationary random graphs

被引：50

作者：

Benjamini, Itai ^{[1
]}

Curien, Nicolas ^{[2
]}

机构：

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

[2] Dma Ens, F-75005 Paris, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2012年 / 17卷

关键词：

Stationary random graph; Simple random walk; Ergodic Theory; Entropy; Liouville Property; LONG-RANGE PERCOLATION; RANDOM-WALKS; INVARIANT PERCOLATION; HARMONIC-FUNCTIONS; TREES; GROWTH; PLANAR; QUADRANGULATION; HOMOGENIZATION; DIMENSION;

D O I：

10.1214/EJP.v17-2401

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 stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show in particular that stationary random graphs of subexponential growth are almost surely Liouville, that is, admit no non constant bounded harmonic functions. Applications include the uniform infinite planar quadrangulation and long-range percolation clusters.

引用

页码：1 / 20

页数：20

共 38 条

[21]

Gurel-Gurevich O., 2012, ANN MATH IN PRESS

[22]

Haggstrom O, 1997, ANN PROBAB, V25, P1423

[23] Hausdorff dimension of the harmonic measure on trees [J].

Kaimanovich, VA .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1998, 18 :631-660

[24] Boundaries and harmonic functions for random walks with random transition probabilities [J].

Kaimanovich, VA ;

Kifer, Y ;

Rubshtein, BZ .

JOURNAL OF THEORETICAL PROBABILITY, 2004, 17 (03) :605-646

[25] RANDOM-WALKS ON DISCRETE-GROUPS - BOUNDARY AND ENTROPY [J].

KAIMANOVICH, VA ;

VERSHIK, AM .

ANNALS OF PROBABILITY, 1983, 11 (03) :457-490

[26]

Kaimanovich VA, 2003, TRENDS MATH, P145

[27]

Kaimanovich VA, 2002, ANN PROBAB, V30, P323

[28]

Kaimanovich VA, 2010, ADV STU P M, V57, P199

[29]

Kamanovich V. A., 1990, Probability theory and mathematical statistics, P573

[30]

KESTEN H, 1986, ANN I H POINCARE-PR, V22, P425

← 1 2 3 4 →