3 papers
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
Vanishing uniqueness thresholds in Voronoi percolation on products
Matteo D'Achille, Jan Grebík, Ali Khezeli +2
We study Poisson--Voronoi percolation and its discrete analogue Bernoulli--Voronoi percolation in spaces with a non-amenable product structure. We develop a new method of proving s…
math.PR2025
Poisson-Voronoi percolation in higher rank
Jan Grebík, Konstantin Recke
We show that the uniqueness thresholds for Poisson-Voronoi percolation in symmetric spaces of connected higher rank semisimple Lie groups with property (T) converge to zero in the…