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Large Poisson-Voronoi cells and Crofton cells

  • Daniel Hug (a1), Matthias Reitzner (a2) and Rolf Schneider (a1)
Abstract

It is proved that the shape of the typical cell of a stationary Poisson-Voronoi tessellation in Euclidean space, under the condition that the volume of the typical cell is large, must be close to spherical, with high probability. The same holds if the volume is replaced by the surface area or other suitable functionals. Similar results are established for the zero cell of a stationary and isotropic Poisson hyperplane tessellation.

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Corresponding author
Postal address: Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstr. 1, D-79104 Freiburg, Germany.
∗∗ Email address: daniel.hug@math.uni-freiburg.de
∗∗∗ Postal address: Institut für Analysis und Technische Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria. Email address: mreitzne@mail.zserv.tuwien.ac.at
∗∗∗∗ Email address: rolf.schneider@math.uni-freiburg.de
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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