On the Arrangement of Cells in Planar STIT and Poisson Line Tessellations
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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.
KeywordsMark-correlation function Neighbourhood of typical cell Pair-correlation function Poisson line tessellation Random tessellation Spatial statistics STIT tessellation Stochastic geometry
AMS 2000 Subject Classification60D05 60G55 62M30
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