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Faces of Poisson–Voronoi mosaics
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  • Published: 21 April 2010

Faces of Poisson–Voronoi mosaics

  • Daniel Hug1 &
  • Rolf Schneider2 

Probability Theory and Related Fields volume 151, pages 125–151 (2011)Cite this article

Abstract

For a stationary Poisson–Voronoi tessellation in Euclidean d-space and for \({k\in \{1,\dots,d\}}\), we consider the typical k-dimensional face with respect to a natural centre function. We express the distribution of this typical k-face in terms of a certain Poisson process of closed halfspaces in a k-dimensional space. Then we show that, under the condition of large inradius, the relative boundary of the typical k-face lies, with high probability, in a narrow spherical annulus.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Karlsruhe Institute of Technology, Kaiserstr. 89-93, 76128, Karlsruhe, Germany

    Daniel Hug

  2. Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, 79104, Freiburg, Germany

    Rolf Schneider

Authors
  1. Daniel Hug
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  2. Rolf Schneider
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Corresponding author

Correspondence to Daniel Hug.

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Cite this article

Hug, D., Schneider, R. Faces of Poisson–Voronoi mosaics. Probab. Theory Relat. Fields 151, 125–151 (2011). https://doi.org/10.1007/s00440-010-0294-7

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  • Received: 13 October 2009

  • Revised: 08 March 2010

  • Published: 21 April 2010

  • Issue Date: October 2011

  • DOI: https://doi.org/10.1007/s00440-010-0294-7

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Keywords

  • Poisson–Voronoi tessellation
  • Typical k-face
  • Spherical shape

Mathematics Subject Classification (2000)

  • 60D05
  • 52A20
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