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  • Contact and Chord Length Distribution Functions of the Poisson-Voronoi Tessellation in High Dimensions

  • Part of
  • L. Muche
  • Journal:
    Advances in Applied Probability / Volume 42 / Issue 1 / March 2010
    Published online by Cambridge University Press:
    01 July 2016, pp. 48-68
    Print publication:
    March 2010
    • Article
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  • In this paper we present formulae for contact distributions of a Voronoi tessellation generated by a homogeneous Poisson point process in the d-dimensional Euclidean space. Expressions are given for the probability density functions and moments of the linear and spherical contact distributions. They are double and simple integral formulae, which are tractable for numerical evaluation and for large d. The special cases d = 2 and d = 3 are investigated in detail, while, for d = 3, the moments of the spherical contact distribution function are expressed by standard functions. Also, the closely related chord length distribution functions are considered.