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Contact and chord length distribution of a stationary Voronoi tessellation

Part of: Stochastic processes Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Lothar Heinrich
Lothar Heinrich*
Affiliation:
University of Augsburg
*
∗ Postal address: Institute of Mathematics, University of Augsburg, Universtätsstr. 14, D-86135 Augsburg, Germany. Email address: heinrich@math.uni-augsburg.de
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Abstract

We give formulae for different types of contact distribution functions for stationary (not necessarily Poisson) Voronoi tessellations in ℝd 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.

Keywords

Voronoi tessellationchord lengthcontact distributionmotion-invariant point processtwo-point Palm distributionPoisson cluster processGibbsian process

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 60G55: Point processes
Secondary: 60G10: Stationary processes 60G60: Random fields
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 30 , Issue 3 , September 1998 , pp. 603 - 618
Copyright
Copyright © Applied Probability Trust 1998 

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