Distributional properties of the typical cell of stationary iterated tessellations

Roland Maier, Johannes Mayer and Volker Schmidt

Mathematical Methods of Operations Research, 2004, vol. 59, issue 2, 287-302

Abstract: Distributional properties are considered of the typical cell of stationary iterated tessellations (SIT), which are generated by stationary Poisson-Voronoi tessellations (SPVT) and stationary Poisson line tessellations (SPLT), respectively. Using Neveu’s exchange formula, the typical cell of SIT can be represented by those cells of its component tessellation hitting the typical cell of its initial tessellation. This provides a simulation algorithm without consideration of limits in space. It has been applied in order to estimate the probability densities of geometric characteristics of the typical cell of SIT generated by SPVT and SPLT. In particular, the probability densities of the number of vertices, the perimeter, and the area of the typical cell of such SIT have been determined. Copyright Springer-Verlag 2004

Keywords: Stochastic geometry; Stationary tessellation; Palm calculus; Typical cell; Iterated tessellation; Poisson Voronoi tessellation; Poisson line tessellation; Simulation (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s001860300326

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