CYLINDERS' PERCOLATION: DECOUPLING AND APPLICATIONS

• 成果类型: Article
• 署名作者: Alves, Caio; Teixeira, Augusto
• 署名单位: United States Department of Energy (DOE); Oak Ridge National Laboratory; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2044
• 发表日期: 2024
• 页码: 3541-3583
• 关键词: vacant set; random interlacements; uniqueness; clusters

摘要

In this paper we establish a strong decoupling inequality for the cylinder's percolation process introduced by Tykesson and Windisch ( Probab. Theory Related Fields 154 (2012) 165-191). This model features a very strong dependency structure, making it difficult to study, and this is why such decoupling inequalities are desirable. It is important to notice that the type of dependencies featured by cylinder's percolation is particularly intricate, given that the cylinders have infinite range (unlike some models like Boolean percolation) while at the same time being rigid bodies (unlike processes such as random interlacements). Our work introduces a new notion of fast decoupling, proves that it holds for the model in question and finishes with an application. More precisely, we prove that for a small enough density of cylinders, a random walk on a connected component of the vacant set is transient for all dimensions d >= 3.