The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane
The distributions of the smallest disks containing the Poisson-Voronoi typical cell and the Crofton cell in the plane
复制标题
包含Poisson-Voronoi典型单元和Crofton单元的最小圆盘在平面上的分布
DOI：
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发表时间：
2002
影响因子：
1.2
通讯作者：
P. Calka
中科院分区：
文献类型：
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作者：
P. Calka
在以二维泊松-沃罗诺伊镶嵌的典型粒子为中心的圆盘中，设R m是与该粒子相关联的多边形单元内所包括的最大圆盘的半径，R M是包含该多边形单元的最小圆盘的半径。本文给出了Rm和RM的联合分布.这个结果是由Stevens，Siegel和Holst关于圆的覆盖性质得到的。同样的方法适用于研究与平面上的泊松线过程相关联的Crofton胞。条件概率P{RM ≥ r + s}的计算|Rm = r}揭示了Poisson-Voronoi典型细胞（以及Crofton细胞）具有“大”内盘的圆形性质。
Among the disks centered at a typical particle of the two-dimensional Poisson-Voronoi tessellation, let R m be the radius of the largest included within the polygonal cell associated with that particle and R M be the radius of the smallest containing that polygonal cell. In this article, we obtain the joint distribution of R m and R M. This result is derived from the covering properties of the circle due to Stevens, Siegel and Holst. The same method works for studying the Crofton cell associated with the Poisson line process in the plane. The computation of the conditional probabilities P{R M ≥ r + s | R m = r} reveals the circular property of the Poisson-Voronoi typical cells (as well as the Crofton cells) having a ‘large’ in-disk.