Selected distributional results for random tessellations

Daniel Hug (Karlsruhe)

Random tessellations have received much attention in recent years.
This is due to progess both in theory and in applications. In the
talk, we start with stationary but not necessarily isotropic Poisson
hyperplane tessellations and describe some distributional properties
of classes of random polytopes (typical and weighted typical
cells and faces) associated with such random tessellations. In the
second part, we address Poisson Voronoi tessellations and highlight
an interesting problem concerning tessellations in high dimensions.