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

Research output: Contribution to journal › Article › Academic › peer-review

3 Citations (Scopus)

39 Downloads (Pure)

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).

Original language	English
Pages (from-to)	2342-2405
Number of pages	64
Journal	Annals of probability
Volume	52
Issue number	6
DOIs	https://doi.org/10.1214/24-AOP1698
Publication status	Published - Nov-2024

Keywords

Hyperbolic
percolation

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10.1214/24-AOP1698

Poisson–Voronoi percolation in the hyperbolic plane with small intensitiesFinal publisher's version, 961 KBLicence: Taverne

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title = "Poisson–Voronoi percolation in the hyperbolic plane with small intensities",

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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N2 - 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).

AB - 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).

KW - Hyperbolic

KW - percolation

UR - https://www.scopus.com/pages/publications/85208276079

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Poisson–Voronoi percolation in the hyperbolic plane with small intensities

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Keywords

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