The Poisson Voronoi Tessellation I. A Basic Identity
The Poisson Voronoi Tessellation I. A Basic Identity
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泊松沃罗诺伊曲面细分 I. 基本恒等式
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
L. Muche
中科院分区：
文献类型：
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作者：
J. Mecke;L. Muche
本文在研究点过程的Palm分布的基础上，给出了IRd中相应Voronoi曲面的点过程和平面截面的点过程与平稳Poisson点过程的基本关系。给出了连接Poisson点过程的分布和Palm分布关于相应Voronoi曲面的顶点的恒等式。边的分布特性进行了讨论。最后，给出了“典型”边和从“典型”顶点随机选择的边的特征的恒等式。
This paper gives basic relations between the stationary Poisson point process and the point process of vertices of the corresponding Voronoi tessellation in IRd and of planar sections through it. The results are based on a study of the Palm distribution of the point process of vertices. An identity is given connecting the distribution of a Poisson point process and the Palm distribution with respect to the vertices of the corresponding Voronoi tessellation. Distributional properties for the edges are discussed. Finally, identities are given for characteristics of the “typical” edge and an edge chosen at random emanating from the “typical” vertex.