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math.PR2025
Critical Poisson hyperplane percolation in hyperbolic space has no unbounded cells
Tillmann Bühler, Anna Gusakova, Konstantin Recke
We show that tessellations of hyperbolic space by isometry-invariant Poisson processes of -dimensional hyperplanes do not have an unbounded cell at the critical intensity. T…
math.PR2025
High-intensity Voronoi percolation on manifolds
Tillmann Bühler, Barbara Dembin, Ritvik Ramanan Radhakrishnan +1
We study Voronoi percolation on a large class of -dimensional Riemannian manifolds, which includes the hyperbolic spaces , . We prove that as the intensit…
math.PR2025
Visibility and intersection density for Boolean models in hyperbolic space
Tillmann Bühler, 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…