arXiv subjects

Benjamin T. Hansen

Publications and source records attributed to Benjamin T. Hansen.

2 recordsLinked to original sources

arXiv2023

Poisson-Voronoi percolation in the hyperbolic plane with small intensities

We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. We show that the critical probability for the existence of an infinite cluster is asymptotically equal to $πλ/3$ as $λ\to0.$ This answers a question of Benjamini and Schramm.

math.PR↗

arXiv2021

The critical probability for Voronoi percolation in the hyperbolic plane tends to $1/2$

We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. We show that the critical probability for the existence of an infinite cluster tends to $1/2$ as the intensity of the Poisson process tends to infinity. This confirms a conjecture of Benjamini and Schramm.

math.PR↗