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Intrinsic volumes of the maximal polytope process in higher dimensional STIT tessellations

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  • Schreiber, Tomasz
  • Thäle, Christoph

Abstract

Stationary and isotropic iteration stable random tessellations are considered, which are constructed by a random process of iterative cell division. The collection of maximal polytopes at a fixed time t within a convex window is regarded and formulas for mean values, variances and a characterization of certain covariance measures are proved. The focus is on the case d>=3, which is different from the planar one, treated separately in Schreiber and Thäle (2010)Â [12]. Moreover, a limit theorem for suitably rescaled intrinsic volumes is established, leading -- in sharp contrast to the situation in the plane -- to a non-Gaussian limit.

Suggested Citation

  • Schreiber, Tomasz & Thäle, Christoph, 2011. "Intrinsic volumes of the maximal polytope process in higher dimensional STIT tessellations," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 989-1012, May.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:5:p:989-1012
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