Structures in supercritical scale-free percolation

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

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3 Citaten (Scopus)
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Samenvatting

Scale-free percolation is a percolation model on Zd 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.

Originele taal-2Engels
Pagina's (van-tot)2569-2604
Aantal pagina's36
TijdschriftThe Annals of Applied Probability
Volume27
Nummer van het tijdschrift4
DOI's
StatusGepubliceerd - 1 aug 2017

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