THE SECTIONAL POISSON VORONOI TESSELLATION IS NOT A VORONOI TESSELLATION

摘要

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 less than or equal to t less than or equal to d-1. Moreover, it is shown that each cell on this intersection is almost surely a non-Voronoi cell. [References: 27]