Structures in supercritical scale-free percolation
| Autor: | Heydenreich, Markus, Hulshof, Tim, Jorritsma, Joost |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Annals of Applied Probability 27(4):2569-2604 (2017) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1214/16-AAP1270 |
| Popis: | 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. Comment: Revised Definition 2.5 and an argument in Section 6, results are unchanged. Correction of minor typos. 29 pages, 7 figures |
| Databáze: | arXiv |
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