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
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
收藏
页码:863 / 870
页数:8
相关论文
共 19 条
[1]   On a coverage process ranging from the Boolean model to the Poisson-Voronoi tessellation with applications to wireless communications [J].
Baccelli, F ;
Blaszczyszyn, B .
ADVANCES IN APPLIED PROBABILITY, 2001, 33 (02) :293-323
[2]   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 [J].
Calka, P .
ADVANCES IN APPLIED PROBABILITY, 2003, 35 (03) :551-562
[3]   The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane [J].
Calka, P .
ADVANCES IN APPLIED PROBABILITY, 2002, 34 (04) :702-717
[4]   RANDOM SUBDIVISIONS OF SPACE INTO CRYSTALS [J].
GILBERT, EN .
ANNALS OF MATHEMATICAL STATISTICS, 1962, 33 (03) :958-&
[5]  
GOLDMAN A, 2003, IN PRESS ANN I H POI
[6]   Calculating the proportion of triangles in a Poisson-Voronoi tessellation of the plane [J].
Hayen, A ;
Quine, M .
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 2000, 67 (04) :351-358
[7]   The proportion of triangles in a Poisson-Voronoi tessellation of the plane [J].
Hayen, A ;
Quine, M .
ADVANCES IN APPLIED PROBABILITY, 2000, 32 (01) :67-74
[8]   MONTE-CARLO ESTIMATES OF THE DISTRIBUTIONS OF THE RANDOM POLYGONS OF THE VORONOI TESSELLATION WITH RESPECT TO A POISSON-PROCESS [J].
HINDE, AL ;
MILES, RE .
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 1980, 10 (3-4) :205-223
[9]   THERMAL-CONDUCTIVITY OF POLYCRYSTALLINE MATERIALS [J].
KUMAR, S ;
SINGH, RN .
JOURNAL OF THE AMERICAN CERAMIC SOCIETY, 1995, 78 (03) :728-736
[10]   PROPERTIES OF A 2-DIMENSIONAL POISSON-VORONOI TESSELATION - A MONTE-CARLO STUDY [J].
KUMAR, S ;
KURTZ, SK .
MATERIALS CHARACTERIZATION, 1993, 31 (01) :55-68