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The sectional Poisson Voronoi tessellation is not a Voronoi tessellation

Published online by Cambridge University Press:  01 July 2016

S. N. Chiu
Affiliation:
TU Bergakademie Freiburg
R. Van De Weygaert
Affiliation:
Canadian Institute for Astrophysics, Sterrewacht Leiden and Max Planck Institute für Astrophysik
D. Stoyan*
Affiliation:
TU Bergakademie Freiburg
*
∗∗∗ Postal address: TU Bergakademie Freiburg, Institut für Stochastik, 09596 Freiburg, Germany.

Abstract

Is the intersection between an arbitrary but fixed plane and the spatial Poisson Voronoi tessellation a planar Voronoi tessellation? In this paper a negative answer is given to this long-standing question in stochastic geometry. The answer remains negative for the intersection between a t-dimensional linear affine space and the d-dimensional Poisson Voronoi tesssellation, where 2 ≦ td − 1. Moreover, it is shown that each cell on this intersection is almost surely a non-Voronoi cell.

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Present address: Department of Mathematics, Hong Kong Baptist University, Waterloo Road, Kowloon, Hong Kong.

∗∗

Present address: Kapteyn Instituut, University of Groningen, Postbus 800, 9700 AV Groningen, The Netherlands.

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