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2 results

  • Approximation Properties of Random Polytopes Associated with Poisson Hyperplane Processes

  • Part of
  • Daniel Hug, Rolf Schneider
  • Journal:
    Advances in Applied Probability / Volume 46 / Issue 4 / December 2014
    Published online by Cambridge University Press:
    22 February 2016, pp. 919-936
    Print publication:
    December 2014
    • Article
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  • We consider a stationary Poisson hyperplane process with given directional distribution and intensity in d-dimensional Euclidean space. Generalizing the zero cell of such a process, we fix a convex body K and consider the intersection of all closed halfspaces bounded by hyperplanes of the process and containing K. We study how well these random polytopes approximate K (measured by the Hausdorff distance) if the intensity increases, and how this approximation depends on the directional distribution in relation to properties of K.