Structures in supercritical scale-free percolation

Heydenreich, Markus; Hulshof, Tim and Jorritsma, Joost (2017): Structures in supercritical scale-free percolation. In: Annals of Applied Probability, Vol. 27, No. 4: pp. 2569-2604

Abstract

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1050-5164
• Language: English