%0 Journal Article %1 1996 %A Chiu, S. N. %A Weygaert, R. Van De %A Stoyan, D. %D 1996 %I Applied Probability Trust %J Advances in Applied Probability %K Poisson-Voronoi spatial_allocation %N 2 %P 356--376 %T The Sectional Poisson Voronoi Tessellation Is Not a Voronoi Tessellation %U http://www.jstor.org/stable/1428061 %V 28 %X 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.

@article{1996, 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.}, added-at = {2009-08-20T01:02:54.000+0200}, author = {Chiu, S. N. and Weygaert, R. Van De and Stoyan, D.}, biburl = {https://www.bibsonomy.org/bibtex/29877439c1d2bd9143c72011b760c3f3a/peter.ralph}, copyright = {Copyright © 1996 Applied Probability Trust}, description = {The Sectional Poisson Voronoi Tessellation Is Not a Voronoi Tessellation}, interhash = {6be91821fa7e74d697a8b3d41823c34b}, intrahash = {9877439c1d2bd9143c72011b760c3f3a}, issn = {00018678}, journal = {Advances in Applied Probability}, jstor_articletype = {primary_article}, jstor_formatteddate = {Jun., 1996}, keywords = {Poisson-Voronoi spatial_allocation}, number = 2, pages = {356--376}, publisher = {Applied Probability Trust}, timestamp = {2010-10-04T23:23:08.000+0200}, title = {The Sectional Poisson Voronoi Tessellation Is Not a Voronoi Tessellation}, url = {http://www.jstor.org/stable/1428061}, volume = 28, year = 1996 }