Methodology and Computing in Applied Probability

, Volume 15, Issue 3, pp 643–654

On the Arrangement of Cells in Planar STIT and Poisson Line Tessellations

Article

Abstract

It is well known that the distributions of the interiors of the typical cells of a Poisson line tessellation and a STIT tessellation with the same parameters coincide. In this paper, differences in the arrangement of the cells in these two tessellation models are investigated. In particular, characteristics of the set of cells neighbouring the typical cell are studied, mainly by simulation. Furthermore, the pair-correlation function and several mark correlation functions of the point processes of cell centres are estimated and compared.

Keywords

Mark-correlation function Neighbourhood of typical cell Pair-correlation function Poisson line tessellation Random tessellation Spatial statistics STIT tessellation Stochastic geometry 

AMS 2000 Subject Classification

60D05 60G55 62M30 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Department of Mathematics and Computer ScienceUniversity of OsnabrückOsnabrückGermany

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