Poisson-Voronoi percolation in the hyperbolic plane with small intensities (2111.04299v3)

Published 8 Nov 2021 in math.PR and math.CO

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 is asymptotically equal to $\pi \lambda/3$ as $\lambda\to0.$ This answers a question of Benjamini and Schramm.

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