Tillmann Buhler

activity

20242026

collaborators

5 papers

math.PR2026

The volume of hyperbolic Poisson zero cells: critical divergence and exact second moment

Tillmann BÃ¼hler, Christoph ThÃ¤le

We investigate the second volume moment of the zero cell $Z_{o}$ of a Poisson hyperplane tessellation with intensity $I^^{3}$ in the $d$ -dimensional hyperbolic space. We focus on the pha…

math.PR2025

Visibility and intersection density for Boolean models in hyperbolic space

Tillmann BÃ¼hler, Daniel Hug, Christoph Thaele

For Poisson particle processes in hyperbolic space we introduce and study concepts analogous to the intersection density and the mean visible volume, which were originally consider…

math.PR2025

Critical Poisson hyperplane percolation in hyperbolic space has no unbounded cells

Tillmann BÃ¼hler, Anna Gusakova, Konstantin Recke

We show that tessellations of hyperbolic space by isometry-invariant Poisson processes of $(d - 1)$ -dimensional hyperplanes do not have an unbounded cell at the critical intensity. T…

math.PR2025

High-intensity Voronoi percolation on manifolds

Tillmann BÃ¼hler, Barbara Dembin, Ritvik Ramanan Radhakrishnan +1

We study Voronoi percolation on a large class of $d$ -dimensional Riemannian manifolds, which includes the hyperbolic spaces $H^{d}$ , $d \geq 2$ . We prove that as the intensit…

math.PR2024

Intersections of Poisson k-flats in hyperbolic space: completing the picture

Tillmann BÃ¼hler, Daniel Hug

In recent years there has been a lot of interest in the study of isometry invariant Poisson processes of $k$ -flats in $d$ -dimensional hyperbolic space $H^{d}$ , for $0\le k\l…