Structures in supercritical scale-free percolation

M. Heydenreich; W.J.T. Hulshof; J. Jorritsma

doi:10.1214/16-AAP1270

Structures in supercritical scale-free percolation

M. Heydenreich
, W.J.T. Hulshof
, J. Jorritsma

Research output: Contribution to journal › Article › Academic › peer-review

21 Citations (Scopus)

123 Downloads (Pure)

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.

Original language	English
Pages (from-to)	2569-2604
Number of pages	36
Journal	Annals of Applied Probability
Volume	27
Issue number	4
DOIs	https://doi.org/10.1214/16-AAP1270
Publication status	Published - 1 Aug 2017

Keywords

Graph distance
Hierarchical clustering
Percolation
Random graphs
Real-world network modeling
Scale-free network
Transience versus recurrence

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10.1214/16-AAP1270

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KW - Graph distance

KW - Hierarchical clustering

KW - Percolation

KW - Random graphs

KW - Real-world network modeling

KW - Scale-free network

KW - Transience versus recurrence

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JF - Annals of Applied Probability

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Structures in supercritical scale-free percolation

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Keywords

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