Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson-Voronoi tessellation and a Poisson line process

被引：36

作者：

Calka, P ^{[1
]}

机构：

[1] Univ Lyon 1, F-69366 Lyon 07, France

来源：

ADVANCES IN APPLIED PROBABILITY | 2003年 / 35卷 / 03期

关键词：

Crofton cell; empirical cell; fundamental domain; Palm distribution; Poisson-Voronoi tessellation; stochastic geometry; typical cell;

D O I：

10.1239/aap/1059486817

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：

In this paper, we give an explicit integral expression for the joint distribution of the number and the respective positions of the sides of the typical cell e of a two-dimensional Poisson-Voronoi tessellation. We deduce from it precise formulae for the distributions of the principal geometric characteristics of e (area, perimeter, area of the fundamental domain). We also adapt the method to the Crofton cell and the empirical (or typical) cell of a Poisson line process.

引用

页码：551 / 562

页数：12