Exponential decay of connection probabilities for subcritical Voronoi percolation in Rd

• 成果类型: Article
• 署名作者: Duminil-Copin, Hugo; Raoufi, Aran; Tassion, Vincent
• 署名单位: University of Geneva; Universite Paris Saclay; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0838-9
• 发表日期: 2019
• 页码: 479-490
• 关键词: phase-transition; sharpness

摘要

We prove that for Voronoi percolation on Rd(d2), there exists pc=pc(d)(0,1) such thatfor p0 such that Pp[0connected to distancen]exp(-cpn),there exists c>0 such that for p>pc,Pp[0connected to infinity]c(p-pc). For dimension 2, this result offers a new way of showing that pc(2)=1/2. This paper belongs to a series of papers using the theory of algorithms to prove sharpness of the phase transition; see [10, 11].