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

Claudia Redenbach () and Christoph Thäle ()
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Claudia Redenbach: University of Kaiserslautern
Christoph Thäle: University of Osnabrück

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 3, 643-654

Abstract: 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; 60D05; 60G55; 62M30 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-011-9273-4

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