ORCID: https://orcid.org/0000-0002-3749-7431
(2023):
Graph distances in scale-free percolation: the logarithmic case.
In: Journal of Applied Probability, Vol. 60, No. 1: pp. 295-313
Abstract
Scale-free percolation is a stochastic model for complex networks. In this spatial random graph model, vertices x,y∈Zd are linked by an edge with probability depending on independent and identically distributed vertex weights and the Euclidean distance |x−y| . Depending on the various parameters involved, we get a rich phase diagram. We study graph distance and compare it to the Euclidean distance of the vertices. Our main attention is on a regime where graph distances are (poly-)logarithmic in the Euclidean distance. We obtain improved bounds on the logarithmic exponents. In the light tail regime, the correct exponent is identified.
Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |
Subjects: | 500 Science > 510 Mathematics |
ISSN: | 0021-9002 |
Language: | English |
Item ID: | 94846 |
Date Deposited: | 03. Mar 2023, 08:17 |
Last Modified: | 13. Aug 2024, 12:44 |