Poisson–Voronoi percolation in the hyperbolic plane with small intensities

Benjamin Hansen, Tobias Müller

Research output: Contribution to journalArticleAcademicpeer-review

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 languageEnglish
Pages (from-to)2342-2405
Number of pages64
JournalAnnals of probability
Volume52
Issue number6
DOIs
Publication statusPublished - Nov-2024

Keywords

  • Hyperbolic
  • percolation

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