Faculté des sciences

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

Schreiber, Tomasz ; Thäle, Christoph

In: Stochastic Processes and their Applications, 2011, p. -

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 View the MathML source 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,... Plus

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    Summary
    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 View the MathML source 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) [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.Keywords: Central limit theory; Integral geometry; Intrinsic volumes; Iteration/Nesting; Markov process; Martingale; Random tessellation; Stochastic stability; Stochastic geometry.