Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces

被引：9
|
作者：
Isokawa, Y [1 ]
机构：
[1] Kagoshima Univ, Fac Educ, Kagoshima 890, Japan
来源：
ADVANCES IN APPLIED PROBABILITY | 2000年 / 32卷 / 03期
关键词：
random tessellation; Voronoi tessellation; mean characteristics; hyperbolic space;
D O I：
10.1017/S000186780001017X
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 study Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces, and give explicit expressions for mean surface area, mean perimeter length, and mean number of vertices of their cells. Furthermore we compare these mean characteristics with those for Poisson-Voronoi tessellations in three-dimensional Euclidean spaces. It is shown that, as the absolute value of the curvature of hyperbolic spaces increases from zero to infinity, these mean characteristics increase monotonically from those for the Euclidean case to infinity.
引用
收藏
页码：648 / 662
页数：15
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