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The Poisson Voronoi Tessellation I. A Basic Identity
Author(s) -
Mecke Joseph,
Muche Lutz
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951760115
Subject(s) - centroidal voronoi tessellation , voronoi diagram , mathematics , point process , vertex (graph theory) , poisson distribution , tessellation (computer graphics) , point (geometry) , poisson point process , combinatorics , enhanced data rates for gsm evolution , identity (music) , geometry , statistics , computer science , physics , artificial intelligence , graph , acoustics
Abstract This paper gives basic relations between the stationary Poisson point process and the point process of vertices of the corresponding Voronoi tessellation in IR d 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.