POISSON-VORONOI PERCOLATION IN THE HYPERBOLIC PLANE WITH SMALL INTENSITIES

• 成果类型: Article
• 署名作者: Hansen, Benjamin; Mueller, Tobias
• 署名单位: University of Groningen
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1698
• 发表日期: 2024
• 页码: 2342-2405
• 关键词: continuum percolation; probabilities; tessellation; visibility; expansion; MODEL

摘要

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 pi A/3 as A-* 0. This answers a question of Benjamini and Schramm ( J. Amer. Math. Soc. 14 (2001) 487-507).