An explicit expression for the distribution of the number of sides of the typical Poisson-Voronoi cell

被引：32

作者：

Calka, P ^{[1
]}

机构：

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

来源：

ADVANCES IN APPLIED PROBABILITY | 2003年 / 35卷 / 04期

关键词：

Palm distribution; Poisson-Voronoi tessellation; stochastic geometry; typical cell;

D O I：

10.1239/aap/1067436323

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 expression for the distribution of the number of sides (or equivalently vertices) of the typical cell of a two-dimensional Poisson-Voronoi tessellation. We use this formula to give a table of numerical values of the distribution function.

引用

页码：863 / 870

页数：8

共 34 条

[1] AVERAGE NUMBER OF SIDES FOR THE NEIGHBORS IN A POISSON-VORONOI TESSELATION
KUMAR, S
KURTZ, SK
WEAIRE, D
PHILOSOPHICAL MAGAZINE B-PHYSICS OF CONDENSED MATTER STATISTICAL MECHANICS ELECTRONIC OPTICAL AND MAGNETIC PROPERTIES, 1994, 69 (03): : 431 - 435
[2] The law of the smallest disk containing the typical Poisson-Voronoi cell
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COMPTES RENDUS MATHEMATIQUE, 2002, 334 (04) : 325 - 330
[3] On the correlation between the volumes of the typical Poisson-Voronoi cell and the typical Stienen sphere
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ADVANCES IN APPLIED PROBABILITY, 2007, 39 (04) : 883 - 892
[4] VOLUME DEGENERACY OF THE TYPICAL CELL AND THE CHORD LENGTH DISTRIBUTION FOR POISSON-VORONOI TESSELLATIONS IN HIGH DIMENSIONS
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ADVANCES IN APPLIED PROBABILITY, 2008, 40 (04) : 919 - 938
[5] Limit theorems for the typical Poisson-Voronoi cell and the Crofton cell with a large inradius
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ANNALS OF PROBABILITY, 2005, 33 (04): : 1625 - 1642
[6] The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane
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ADVANCES IN APPLIED PROBABILITY, 2002, 34 (04) : 702 - 717
[7] Accurate representation of the distributions of the 3D Poisson-Voronoi typical cell geometrical features
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[8] Load on the Typical Poisson Voronoi Cell With Clustered User Distribution
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Dhillon, Harpreet S.
IEEE WIRELESS COMMUNICATIONS LETTERS, 2020, 9 (09) : 1361 - 1365
[9] Distance from the Nucleus to a Uniformly Random Point in the 0-Cell and the Typical Cell of the Poisson-Voronoi Tessellation
Mankar, Praful D.
Parida, Priyabrata
Dhillon, Harpreet S.
Haenggi, Martin
JOURNAL OF STATISTICAL PHYSICS, 2020, 181 (05) : 1678 - 1698
[10] The second volume moment of the typical cell and higher moments of edge lengths of the spatial Poisson-Voronoi tessellation
Muche, Lutz
Ballani, Felix
MONATSHEFTE FUR MATHEMATIK, 2011, 163 (01): : 71 - 80

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