Probability Theory and Related Fields

, Volume 151, Issue 1, pp 125–151

Faces of Poisson–Voronoi mosaics

Article

DOI: 10.1007/s00440-010-0294-7

Cite this article as:
Hug, D. & Schneider, R. Probab. Theory Relat. Fields (2011) 151: 125. doi:10.1007/s00440-010-0294-7
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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.

Keywords

Poisson–Voronoi tessellation Typical k-face Spherical shape 

Mathematics Subject Classification (2000)

60D05 52A20 

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Mathematisches InstitutAlbert-Ludwigs-UniversitätFreiburgGermany