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Distributional properties of the typical cell of stationary iterated tessellations

Author

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  • Roland Maier
  • Johannes Mayer
  • Volker Schmidt

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

Suggested Citation

  • Roland Maier & Johannes Mayer & Volker Schmidt, 2004. "Distributional properties of the typical cell of stationary iterated tessellations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 287-302, June.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:2:p:287-302
    DOI: 10.1007/s001860300326
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    Citations

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    Cited by:

    1. C. Gloaguen & F. Fleischer & H. Schmidt & V. Schmidt, 2005. "Simulation of typical Cox–Voronoi cells with a special regard to implementation tests," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 357-373, December.
    2. David Neuhäuser & Christian Hirsch & Catherine Gloaguen & Volker Schmidt, 2016. "A Stochastic Model for Multi-Hierarchical Networks," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1129-1151, December.

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