English

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 dd-dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the kk-faces of the tessellation by a suitable size functional, we determine a limit distribution for the shape of the typical kk-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}
}
R2 v1 2026-06-23T03:35:39.210Z