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Small faces in stationary Poisson hyperplane tessellations

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  • Rolf Schneider

Abstract

We consider the tessellation induced by a stationary Poisson hyperplane process in d‐dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the k‐faces of the tessellation by a suitable size functional, we determine a limit distribution for the shape of the typical k‐face, under the condition of given size and this tending to zero. The limit distribution is concentrated on simplices. This extends a result of Gilles Bonnet.

Suggested Citation

  • Rolf Schneider, 2019. "Small faces in stationary Poisson hyperplane tessellations," Mathematische Nachrichten, Wiley Blackwell, vol. 292(8), pages 1811-1822, August.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:8:p:1811-1822
    DOI: 10.1002/mana.201800366
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