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1 results

  • Weighted faces of Poisson hyperplane tessellations

  • Part of
  • Rolf Schneider
  • Journal:
    Advances in Applied Probability / Volume 41 / Issue 3 / September 2009
    Published online by Cambridge University Press:
    01 July 2016, pp. 682-694
    Print publication:
    September 2009
    • Article
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  • We study lower-dimensional volume-weighted typical faces of a stationary Poisson hyperplane tessellation in d-dimensional Euclidean space. After showing how their distribution can be derived from that of the zero cell, we obtain sharp lower and upper bounds for the expected vertex number of the volume-weighted typical k-face (k=2,…,d). The bounds are respectively attained by parallel mosaics and by isotropic tessellations. We conclude with a remark on expected face numbers and expected intrinsic volumes of the zero cell.