Non-vanishing uniqueness threshold for hyperbolic Poisson-Voronoi percolation in dimension at least three

Matthias Irlbeck, Tobias Müller

We study the threshold for the existence of exactly one unbounded cluster for Poisson-Voronoi percolation on the $d$-dimensional hyperbolic space ${\mathbb{H}}^d$ for $d\ge 3$. By r…