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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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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DOI: https://doi.org/10.1007/s00440-010-0294-7
Keywords
- Poisson–Voronoi tessellation
- Typical k-face
- Spherical shape
Mathematics Subject Classification (2000)
- 60D05
- 52A20