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

Hansen Benjamin T. | Zendy; Müller Tobias | Zendy

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

Author(s) -

Hansen Benjamin T.,

Müller Tobias

Publication year - 2022

Publication title -

random structures and algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.314

H-Index - 69

eISSN - 1098-2418

pISSN - 1042-9832

DOI - 10.1002/rsa.21018

Subject(s) - voronoi diagram , percolation (cognitive psychology) , mathematics , point process , poisson distribution , plane (geometry) , infinity , hyperbolic tree , poisson process , hyperbolic geometry , conjecture , poisson point process , mathematical analysis , continuum percolation theory , statistical physics , percolation critical exponents , combinatorics , geometry , physics , statistics , critical exponent , scaling , differential geometry , biology , neuroscience

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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