Random walks on infinite self-similar graphs

被引：3

作者：

Neunhaeuserer, J.

机构：

[1] Goslar, 38640

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2007年 / 12卷

关键词：

random walk; graph;

D O I：

10.1214/EJP.v12-448

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 introduce a class of rooted infinite self-similar graphs containing the well known Fibonacci graph and graphs associated with Pisot numbers. We consider random walks on these graphs and study their entropy and their limit measures. We prove that every infinite self-similar graph has a random walk of full entroopy and that the limit measures of this random walks are absolutely continuous.

引用

页码：1258 / 1275

页数：18

共 15 条

[1] 24Walters P., 2000, An Introduction to Ergodic Theory, V79
[2] ALEXANDER JC, 1991, J LOND MATH SOC, V44, P121
[3] Bertin M.J., 1992, PISOT SALEM NUMBERS
[4] Denker M., 1976, LECT NOTES MATH, V527
[5] Falconer K., 2004, FRACTAL GEOMETRY MAT
[6] GARSIA AM, 1962, T AM MATH SOC, V10, P409
[7] Combinatorial and arithmetical properties of linear numeration systems
Grabner, PJ
Kirschenhofer, P
Tichy, RF
[J]. COMBINATORICA, 2002, 22 (02) : 245 - 267
[8] Katok A., 1995, INTRO MODERN THEORY, DOI 10.1017/CBO9780511809187
[9] Growth of self-similar graphs
Krön, B
[J]. JOURNAL OF GRAPH THEORY, 2004, 45 (03) : 224 - 239
[10] Asymptotics of the transition probabilities of the simple random walk on self-similar graphs
Krön, B
Teufl, E
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (01) : 393 - 414

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