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Contact and chord length distribution of a stationary Voronoi tessellation

  • Lothar Heinrich (a1)

Abstract

We give formulae for different types of contact distribution functions for stationary (not necessarily Poisson) Voronoi tessellations in ℝ d in terms of the Palm void probabilities of the generating point process. Moreover, using the well-known relationship between the linear contact distribution and the chord length distribution we derive a closed form expression for the mean chord length in terms of the two-point Palm distribution and the pair correlation function of the generating point process. The results obtained are specified for Voronoi tessellations generated by Poisson cluster and Gibbsian processes, respectively.

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Postal address: Institute of Mathematics, University of Augsburg, Universtätsstr. 14, D-86135 Augsburg, Germany. Email address: heinrich@math.uni-augsburg.de

References

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Contact and chord length distribution of a stationary Voronoi tessellation

  • Lothar Heinrich (a1)

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