Gracar, P orcid.org/0000-0001-8340-8340, Lüchtrath, L and Mörters, P (2021) Percolation phase transition in weight-dependent random connection models. Advances in Applied Probability, 53 (4). pp. 1090-1114. ISSN 0001-8678
Abstract
We investigate spatial random graphs defined on the points of a Poisson process in d-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the weight and position of the points, we form an edge between any pair of points independently with a probability depending on the two weights of the points and their distance. Preference is given to short edges and connections to vertices with large weights. We characterize the parameter regime where there is a non-trivial percolation phase transition and show that it depends not only on the power-law exponent of the degree distribution but also on a geometric model parameter. We apply this result to characterize robustness of age-based spatial preferential attachment networks.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2021. Published by Cambridge University Press on behalf of Applied Probability Trust. This article has been published in a revised form in https://doi.org/10.1017/apr.2021.13. This version is free to view and download for private research and study only. Not for re-distribution or re-use. |
Keywords: | Subcritical regime, random geometric graph, Boolean model, scale-free percolation, long-range percolation, spatial network, robustness, age-based spatial preferential attachment |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 02 Jun 2023 09:13 |
Last Modified: | 02 Jun 2023 13:10 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/apr.2021.13 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:199850 |