Recurrence of the Zd-valued infinite snake via unimodularity

被引：4

作者：

Benjamini, Itai ^{[1
]}

Curien, Nicolas ^{[2
]}

机构：

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

[2] ENS, DMA, F-75005 Paris, France

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2012年 / 17卷

关键词：

Galton-Watson trees; random snake; mass-transport; unimodular random graph; BRANCHING RANDOM-WALK; TREES; BEHAVIOR; CLUSTER;

D O I：

10.1214/ECP.v17-1700

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 use the concept of unimodular random graph to show that the branching simple random walk on Z(d) indexed by a critical geometric Galton-Watson tree conditioned to survive is recurrent if and only if d <= 4.

引用

页码：1 / 10

页数：10

共 22 条

[1] TREE-BASED MODELS FOR RANDOM DISTRIBUTION OF MASS [J].

ALDOUS, D .

JOURNAL OF STATISTICAL PHYSICS, 1993, 73 (3-4) :625-641

[2]

Aldous D., 1991, ANN APPL PROBAB, V1, P228

[3] Processes on unimodular random networks [J].

Aldous, David ;

Lyons, Russell .

ELECTRONIC JOURNAL OF PROBABILITY, 2007, 12 :1454-1508

[4]

[Anonymous], 1999, LECT MATH

[5]

[Anonymous], PROBABILITY TR UNPUB

[6]

[Anonymous], 1972, GRUNDLEHREN MATH WIS

[7] Random walk on the incipient infinite cluster on trees [J].

Barlow, Martin T. ;

Kumagai, Takashi .

ILLINOIS JOURNAL OF MATHEMATICS, 2006, 50 (01) :33-65

[8] Group-invariant percolation on graphs [J].

Benjamini, I ;

Lyons, R ;

Peres, Y ;

Schramm, O .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 1999, 9 (01) :29-66

[9] MARKOV-CHAINS INDEXED BY TREES [J].

BENJAMINI, I ;

PERES, Y .

ANNALS OF PROBABILITY, 1994, 22 (01) :219-243

[10]

Benjamini I., 2001, ELECT J PROBAB, V6

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