Poisson cylinders in hyperbolic space

被引：2

作者：

Broman, Erik ^{[1
]}

Tykesson, Johan ^{[2
,3
]}

机构：

[1] Uppsala Univ, Dept Math, S-75105 Uppsala, Sweden

[2] Chalmers Univ Technol, Dept Math, Div Math Stat, Gothenburg, Sweden

[3] Gothenburg Univ, S-41124 Gothenburg, Sweden

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2015年 / 20卷

基金：

瑞典研究理事会;

关键词：

Poisson cylinders; hyperbolic space; continuum percolation; RANDOM INTERLACEMENTS; PERCOLATION; PLANE;

D O I：

10.1214/EJP.v20-3645

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 consider the Poisson cylinder model in d-dimensional hyperbolic space. We show that in contrast to the Euclidean case, there is a phase transition in the connectivity of the collection of cylinders as the intensity parameter varies. We also show that for any non-trivial intensity, the diameter of the collection of cylinders is infinite.

引用

页码：1 / 25

页数：25

共 17 条

[1] Ahlfors Lars V., 1981, ORDWAY PROFESSORSHIP
[2] Beardon Alan F., 1983, GRADUATE TEXTS MATH, V91
[3] Percolation in the hyperbolic plane
Benjamini, I
Schramm, O
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 14 (02) : 487 - 507
[4] Benjamini I, 2009, ALEA-LAT AM J PROBAB, V6, P323
[5] The critical probability for random Voronoi percolation in the plane is 1/2
Bollobas, Bela
Riordan, Oliver
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2006, 136 (03) : 417 - 468
[6] Broman Erik, ANN I H POI IN PRESS
[7] Cannon James W., 1997, Flav Geom., V31, P2
[8] Grimmett G. R., 1999, Percolation, V2nd ed.
[9] Uniqueness and non-uniqueness in percolation theory
Haggstrom, Olle
Jonasson, Johan
[J]. PROBABILITY SURVEYS, 2006, 3 : 289 - 344
[10] Li S., 2011, Asian Journal of Mathematics and Statistics, V4, P66

← 1 2 →