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arXiv · 1604.08180

Structures in supercritical scale-free percolation

Markus Heydenreich·Tim Hulshof·Joost Jorritsma
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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 vs. 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. 2016-04-27. Structures in supercritical scale-free percolation. https://doi.org/10.1214/16-aap1270

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