Small faces in stationary Poisson hyperplane tessellations
Metric Geometry
2018-08-17 v1
Abstract
We consider the tessellation induced by a stationary Poisson hyperplane process in -dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the -faces of the tessellation by a suitable size functional, we determine a limit distribution for the shape of the typical -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.
Keywords
Cite
@article{arxiv.1808.05432,
title = {Small faces in stationary Poisson hyperplane tessellations},
author = {Rolf Schneider},
journal= {arXiv preprint arXiv:1808.05432},
year = {2018}
}