Faces of Poisson-Voronoi mosaics

被引：1

作者：

Hug, Daniel ^{[1
]}

Schneider, Rolf ^{[2
]}

机构：

[1] Karlsruhe Inst Technol, Dept Math, D-76128 Karlsruhe, Germany

[2] Univ Freiburg, Inst Math, D-79104 Freiburg, Germany

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2011年 / 151卷 / 1-2期

关键词：

Poisson-Voronoi tessellation; Typical k-face; Spherical shape; CROFTON CELL;

D O I：

10.1007/s00440-010-0294-7

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：

For a stationary Poisson-Voronoi tessellation in Euclidean d-space and for k is an element of {1, ... , d}, we consider the typical k-dimensional face with respect to a natural centre function. We express the distribution of this typical k-face in terms of a certain Poisson process of closed halfspaces in a k-dimensional space. Then we show that, under the condition of large inradius, the relative boundary of the typical k-face lies, with high probability, in a narrow spherical annulus.

引用

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页码：125 / 151

页数：27

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