The sectional Poisson Voronoi tessellation is not a Voronoi tessellation

The sectional Poisson Voronoi tessellation is not a Voronoi tessellation

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Article ID: iaor1997786
Country: United Kingdom
Volume: 28
Issue: 2
Start Page Number: 356
End Page Number: 376
Publication Date: Jun 1996
Journal: Advances in Applied Probability
Authors: , ,
Keywords: probability
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 tessellation, where 2•t•d-1. Moreover, it is shown that each cell on this intersection is almost surely a non-Voronoi cell.

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