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 $\pi \lambda/3$ as $\lambda\to0.$ This answers a question of Benjamini and Schramm.

Benjamin T. Hansen

Tobias Müller

The Annals of Probability

概率年鉴发表现代概率论的研究论文，它与其他数学领域的关系，以及它在物理和生物科学中的应用。重点是重要性、兴趣和独创性——形式上的新颖性和正确性不足以发表。 《年鉴》还将发表权威的评论论文和对蓬勃发展领域的调查。

The Annals of Probability publishes research papers on modern probability theory, exploring its connections with other areas of mathematics and its applications in physical and biological sciences. The journal emphasizes the importance, interest, and originality of the papers; mere novelty and correctness are insufficient for publication. Additionally, the Annals will publish authoritative review papers and surveys of thriving fields.

《Annals of Probability》发表现代概率论的研究论文，探讨其与其他数学领域的关系，以及在物理和生物科学中的应用。期刊重点关注论文的重要性、趣味性和独创性，单纯的形式新颖性和正确性不足以满足发表要求。此外，《Annals of Probability》还会刊登权威的评论论文和对快速发展的领域的综述。

Category	Quartile
数学	1
数学, 统计学与概率论	1

Poisson–Voronoi percolation in the hyperbolic plane with small intensities

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Journal Info

Category	Quartile
STATISTICS & PROBABILITY	1