The critical probability for Voronoi percolation in the hyperbolic plane tends to 1/2 |
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Authors: | Benjamin T. Hansen,Tobias Mü ller |
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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 [5]. |
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Keywords: | hyperbolic plane percolation voronoi tessellation |
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