Structures in supercritical scale-free percolation

Heydenreich, Markus; Hulshof, Tim und Jorritsma, Joost (2017): Structures in supercritical scale-free percolation. In: Annals of Applied Probability, Bd. 27, Nr. 4: S. 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1050-5164
• Sprache: Englisch