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

Benjamin T. Hansen*, Tobias Müller

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
117 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 tends to 1/2 as the intensity of the Poisson process tends to infinity. This confirms a conjecture of Benjamini and Schramm [5].

Original languageEnglish
Pages (from-to)54-67
Number of pages14
JournalRandom Structures and Algorithms
Volume60
Issue number1
DOIs
Publication statusPublished - Jan-2022

Keywords

  • hyperbolic plane
  • percolation
  • voronoi tessellation

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