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August 2017 Structures in supercritical scale-free percolation
Markus Heydenreich, Tim Hulshof, Joost Jorritsma
Ann. Appl. Probab. 27(4): 2569-2604 (August 2017). DOI: 10.1214/16-AAP1270

Abstract

Scale-free percolation is a percolation model on $\mathbb{Z}^{d}$ 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.

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Markus Heydenreich. Tim Hulshof. Joost Jorritsma. "Structures in supercritical scale-free percolation." Ann. Appl. Probab. 27 (4) 2569 - 2604, August 2017. https://doi.org/10.1214/16-AAP1270

Information

Received: 1 May 2016; Revised: 1 November 2016; Published: August 2017
First available in Project Euclid: 30 August 2017

zbMATH: 1373.60158
MathSciNet: MR3693534
Digital Object Identifier: 10.1214/16-AAP1270

Subjects:
Primary: 05C80, 60K35, 82B20

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.27 • No. 4 • August 2017
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