11 papers · 1 filter
Face volume densities of positive-intensity and ideal Poisson--Voronoi tessellations in hyperbolic spaces
Matteo D'Achille, Christoph Thäle
We determine analytically for all the -volume densities of a Poisson--Voronoi tessellation of intensity in the -dimensional hyperbolic space o…
Visibility in the Boolean Model on Harmonic Manifolds
Enkelejd Hashorva, Christoph Thäle
In Poisson Boolean models with deterministic ball grains, the directional visible range from an uncovered point is known to be exponentially distributed in Euclidean and real hyper…
Central Limit Theorem for Random Partial Sphere Coverings in High Dimensions
Steven Hoehner, Christoph Thäle
We study a random partial covering model on the -dimensional unit sphere, where spherical caps are placed independently and uniformly at random, each covering a surface…
The volume of hyperbolic Poisson zero cells: critical divergence and exact second moment
Tillmann Bühler, Christoph Thäle
We investigate the second volume moment of the zero cell of a Poisson hyperplane tessellation with intensity in the -dimensional hyperbolic space. We focus on the pha…
Random convex chains through the lens of analytic combinatorics
Florian Besau, Christoph Thäle
Consider the triangle with vertices , , and . The lower boundary of the convex hull of , , together with independent uniformly distribute…
Wicksell's corpuscle problem in spaces of constant curvature
Panagiotis Spanos, Christoph Thäle
In this paper, we study Wicksell's corpuscle problem in spaces of constant curvature, thus extending the classical Euclidean framework. We consider a particle process of balls with…