STRUCTURES IN SUPERCRITICAL SCALE-FREE PERCOLATION

• 成果类型: Article
• 署名作者: Heydenreich, Markus; Hulshof, Tim; Jorritsma, Joost
• 署名单位: University of Munich; Eindhoven University of Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1270
• 发表日期: 2017
• 页码: 2569-2604
• 关键词: long-range percolation; infinite cluster; MODEL; BEHAVIOR; walk

摘要

Scale-free percolation is a percolation model on Z(d) which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience versus recurrence for dimension 1 and 2 and give sufficient conditions for transience in dimension 3 and higher. Finally, we show the existence of a hierarchical structure for parameters where vertices have degrees with infinite variance and obtain bounds on the cluster density.