Random walks on stochastic hyperbolic half planar triangulations

被引：6

作者：

Angel, Omer ^{[1
]}

Nachmias, Asaf ^{[2
]}

Ray, Gourab ^{[3
]}

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V5Z 1M9, Canada

[2] Tel Aviv Univ, Nachmias, IL-69978 Tel Aviv, Israel

[3] Univ Cambridge, DPMMS, Cambridge CB2 1TN, England

来源：

RANDOM STRUCTURES & ALGORITHMS | 2016年 / 49卷 / 02期

基金：

英国工程与自然科学研究理事会; 加拿大自然科学与工程研究理事会;

关键词：

random graphs; planar maps; anchored expansion; positive speed; hyperbolic graph; MARKOV-CHAINS; ISOPERIMETRIC-INEQUALITIES; CLUSTER; GRAPHS; MAPS;

D O I：

10.1002/rsa.20625

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in (Angel and Ray, Ann Probab, in press). We show that almost surely the walker escapes the boundary of the map in positive speed and that the return probability to the starting point after n steps scales like exp(-cn1/3) (c) 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 213-234, 2016

引用

页码：213 / 234

页数：22

共 29 条

[1] Growth and percolation on the uniform infinite planar triangulation [J].

Angel, O .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2003, 13 (05) :935-974

[2] CLASSIFICATION OF HALF-PLANAR MAPS [J].

Angel, Omer ;

Ray, Gourab .

ANNALS OF PROBABILITY, 2015, 43 (03) :1315-1349

[3] Percolations on random maps I: Half-plane models [J].

Angel, Omer ;

Curien, Nicolas .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2015, 51 (02) :405-431

[4] Uniform infinite planar triangulations [J].

Angell, O ;

Schramm, O .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 241 (2-3) :191-213

[5]

[Anonymous], 2009, American Mathematical Soc.

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

Barlow, Martin T. ;

Kumagai, Takashi .

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

[7]

Benjamini I, 1999, SYM MATH, V39, P56

[8]

Benjamini I., 2001, Electron. J. Probab., V6, P13, DOI DOI 10.1214/EJP.V6-96

[9] Simple random walk on the uniform infinite planar quadrangulation: subdiffusivity via pioneer points [J].

Benjamini, Itai ;

Curien, Nicolas .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2013, 23 (02) :501-531

[10]

Benjamini Itai, 2014, ARXIV14094312

← 1 2 3 →