Structures in supercritical scale-free percolation
Probability
2018-01-11 v2 Combinatorics
Abstract
Scale-free percolation is a percolation model on 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.
Cite
@article{arxiv.1604.08180,
title = {Structures in supercritical scale-free percolation},
author = {Markus Heydenreich and Tim Hulshof and Joost Jorritsma},
journal= {arXiv preprint arXiv:1604.08180},
year = {2018}
}
Comments
Revised Definition 2.5 and an argument in Section 6, results are unchanged. Correction of minor typos. 29 pages, 7 figures