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Precise formulae for the distributions of the principal geometric characteristics of the typical cells of a two-dimensional Poisson-Voronoi tessellation and a Poisson line process

Part of: Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Pierre Calka
Pierre Calka*
Affiliation:
Université Claude Bernard Lyon 1
*
∗ Postal address: Université Claude Bernard Lyon 1, LaPCS, Bât. B, Domaine de Gerland, 50, avenue Tony-Garnier, F-69366 Lyon Cedex 07, France. Email address: pierre.calka@univ-lyon1.fr
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Abstract

In this paper, we give an explicit integral expression for the joint distribution of the number and the respective positions of the sides of the typical cell 𝒞 of a two-dimensional Poisson-Voronoi tessellation. We deduce from it precise formulae for the distributions of the principal geometric characteristics of 𝒞 (area, perimeter, area of the fundamental domain). We also adapt the method to the Crofton cell and the empirical (or typical) cell of a Poisson line process.

Keywords

Crofton cellempirical cellfundamental domainPalm distributionPoisson-Voronoi tessellationstochastic geometrytypical cell

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 35 , Issue 3 , September 2003 , pp. 551 - 562
Copyright
Copyright © Applied Probability Trust 2003 

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