Calculating the proportion of triangles in a Poisson-Voronoi tessellation of the plane

被引:3
作者
Hayen, A [1 ]
Quine, M [1 ]
机构
[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia
关键词
stochastic geometry; numerical integration; Poisson; Voronoi; tessellation; pain probability; triangle; fundamental region;
D O I
10.1080/00949650008812050
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
The proportion of triangles in a Poisson-Voronoi tessellation has been recently represented as a five-fold integral. Here we give a simpler representation, reduce it to a fourfold integral and discuss its numerical evaluation.
引用
收藏
页码:351 / 358
页数:8
相关论文
共 5 条
[1]   DCUHRE - AN ADAPTIVE MULTIDIMENSIONAL INTEGRATION ROUTINE FOR A VECTOR OF INTEGRALS [J].
BERNTSEN, J ;
ESPELID, TO ;
GENZ, A .
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1991, 17 (04) :452-456
[2]   AN ADAPTIVE ALGORITHM FOR THE APPROXIMATE CALCULATION OF MULTIPLE INTEGRALS [J].
BERNTSEN, J ;
ESPELID, TO ;
GENZ, A .
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1991, 17 (04) :437-451
[3]   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
[4]   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
[5]   ESTIMATES FOR DISTRIBUTIONS OF THE VORONOI POLYGONS GEOMETRIC CHARACTERISTICS [J].
ZUYEV, SA .
RANDOM STRUCTURES & ALGORITHMS, 1992, 3 (02) :149-162