Poisson–Voronoi percolation in the hyperbolic plane with small intensities

Benjamin Hansen; Tobias Müller

doi:10.1214/24-AOP1698

Poisson–Voronoi percolation in the hyperbolic plane with small intensities

Benjamin Hansen, Tobias Müller

Probability and Statistics

Onderzoeksoutput › Academic › peer review

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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→0. This answers a question of Benjamini and Schramm (J. Amer. Math. Soc. 14 (2001) 487–507).

Originele taal-2	English
Pagina's (van-tot)	2342-2405
Aantal pagina's	64
Tijdschrift	Annals of probability
Volume	52
Nummer van het tijdschrift	6
DOI's	https://doi.org/10.1214/24-AOP1698
Status	Published - nov.-2024

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Poisson–Voronoi percolation in the hyperbolic plane with small intensities
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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 is asymptotically equal to πλ/3 as λ→0. This answers a question of Benjamini and Schramm (J. Amer. Math. Soc. 14 (2001) 487–507).",

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Poisson–Voronoi percolation in the hyperbolic plane with small intensities

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