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

Benjamin T. Hansen; Tobias Müller

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arXiv · 2004.01464

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

Benjamin T. Hansen·Tobias Müller

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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.

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Benjamin T. Hansen, Tobias Müller. 2020-04-03. The critical probability for Voronoi percolation in the hyperbolic plane tends to $1/2$. https://arxiv.org/abs/2004.01464

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