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

Benjamin T. Hansen; Tobias Müller

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

Probability 2021-02-17 v3 Combinatorics

Authors: Benjamin T. Hansen , Tobias Müller

Abstract

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.

Keywords

Voronoi percolation hyperbolic plane critical probability Poisson point process infinite cluster

Cite

@article{arxiv.2004.01464,
  title  = {The critical probability for Voronoi percolation in the hyperbolic plane tends to $1/2$},
  author = {Benjamin T. Hansen and Tobias Müller},
  journal= {arXiv preprint arXiv:2004.01464},
  year   = {2021}
}

Comments

15 pages, 6 figures, to be published in Random Structures and Algorithms, very minor corrections since the last version

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

Abstract

Keywords

Cite

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