Small faces in stationary Poisson hyperplane tessellations

Rolf Schneider

Mathematische Nachrichten, 2019, vol. 292, issue 8, 1811-1822

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.

Date: 2019
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