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 |
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Pages (from-to) | 2342-2405 |
Number of pages | 64 |
Journal | Annals of probability |
Volume | 52 |
Issue number | 6 |
DOIs | |
Publication status | Published - Nov-2024 |
Keywords
- Hyperbolic
- percolation