CROSSING PROBABILITIES FOR VORONOI PERCOLATION

• 成果类型: Article
• 署名作者: Tassion, Vincent
• 署名单位: University of Geneva
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1052
• 发表日期: 2016
• 页码: 3385-3398
• 关键词: continuum percolation; THEOREM

摘要

We prove that the standard Russo-Seymour-Welsh theory is valid for Voronoi percolation. This implies that at criticality the crossing probabilities for rectangles are bounded by constants depending only on their aspect ratio. This result has many consequences, such as the polynomial decay of the one arm event at criticality.