NEW MEAN VALUES FOR HOMOGENEOUS SPATIAL TESSELLATIONS THAT ARE STABLE UNDER ITERATION

Christoph Thäle; Viola Weiss

doi:10.5566/ias.v29.p143-157

Authors

Christoph Thäle Département de Mathématiques, Chemin du Musée 23, Université de Fribourg, CH-1700 Fribourg, Suisse
Viola Weiss Fachbereich Grundlagenwissenschaften, Carl-Zeiss-Promenade 2, Fachhochschule Jena, D-07745 Jena, Deutschland

DOI:

https://doi.org/10.5566/ias.v29.p143-157

Keywords:

convex geometry, iteration/nesting, mean values, random tessellation, spatial statistics, stochastic geometry, zonoid

Abstract

Homogeneous random tessellations in the 3-dimensional Euclidean space are considered that are stable under iteration – STIT tessellations. A classification of vertices, segments and flats is introduced and a couple of new metric and topological mean values for them and for the typical cell are calculated. They are illustrated by two examples, the isotropic and the cuboid case. Several extremum problems for these mean values are solved with the help of techniques from convex geometry by introducing an associated zonoid for STIT tessellations.