2018/08/16 by Schneider, Rolf
#60D05 #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1808.05432
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 small size and this tending to zero. The limit distribution is concentrated on simplices. This extends a result of Gilles Bonnet.