The sectional Poisson Voronoi tessellation is not a Voronoi tessellation

Sung Nok CHIU*, R. Van De Weygaert, D. Stoyan

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

16 Citations (Scopus)

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≦t≦d-1. Moreover, it is shown that each cell on this intersection is almost surely a non-Voronoi cell.

Original languageEnglish
Pages (from-to)356-376
Number of pages21
JournalAdvances in Applied Probability
Volume28
Issue number2
DOIs
Publication statusPublished - Jun 1996

Scopus Subject Areas

  • Statistics and Probability
  • Applied Mathematics

User-Defined Keywords

  • Poisson process
  • Sectional Voronoi tessellation
  • Stochastic geometry
  • Voronoi tessellation

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