Abstract
Scale-free percolation is a percolation model on 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.
Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |
Subjects: | 500 Science > 510 Mathematics |
ISSN: | 1050-5164 |
Language: | English |
Item ID: | 53459 |
Date Deposited: | 14. Jun 2018, 09:53 |
Last Modified: | 13. Aug 2024, 12:42 |