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

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  • Schreiber, Tomasz
  • Thäle, Christoph
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 121 (2011)
    Issue (Month): 5 (May)
    Pages: 989-1012

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    Handle: RePEc:eee:spapps:v:121:y:2011:i:5:p:989-1012

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    Related research

    Keywords: Central limit theory Integral geometry Intrinsic volumes Iteration/Nesting Markov process Martingale Random tessellation Stochastic stability Stochastic geometry;

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