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

Part of: Geometric probability and stochastic geometry General convexity

Published online by Cambridge University Press:  01 July 2016

L. Muche
L. Muche*
Affiliation:
Fraunhofer Institute for Integrated Circuits
*
∗ Postal address: Fraunhofer Institute for Integrated Circuits, EAS Dresden, Zeunerstraße 38, D-01069 Dresden, Germany. Email address: lutz.muche@eas.iis.fraunhofer.de
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Abstract

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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.

Keywords

Probability density functionmomentlinear and spherical contact distribution functionschord length

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 52A22: Random convex sets and integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 42 , Issue 1 , March 2010 , pp. 48 - 68
Copyright
Copyright © Applied Probability Trust 2010 

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