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Numerical and analytical computation of some second-order characteristics of spatial Poisson-Voronoi tessellations. (English) Zbl 0912.60023

The main goal of this paper is to calculate the pair correlation function of the point process of nodes of the three-dimensional stationary Poisson-Voronoi tessellation. Furthermore the asymptotic for the variance of the number of nodes in an expanding region and the variance of the number of vertices of the typical Poisson-Voronoi polyhedron are obtained.

MSC:

60D05 Geometric probability and stochastic geometry
62F12 Asymptotic properties of parametric estimators
62F25 Parametric tolerance and confidence regions
65C99 Probabilistic methods, stochastic differential equations
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