Gracar, P orcid.org/0000-0001-8340-8340, Heydenreich, M, Mönch, C et al. (1 more author) (2022) Recurrence versus transience for weight-dependent random connection models. Electronic Journal of Probability, 27. EJP748. ISSN 1083-6489
Abstract
We investigate random graphs on the points of a Poisson process in d-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point carries an independent random mark and given marks and positions of the points we form an edge between two points independently with a probability depending via a kernel on the two marks and the distance of the points. Different kernels allow the mark to play different roles, like weight, radius or birth time of a vertex. The kernels depend on a parameter γ, which determines the power-law exponent of the degree distributions. A further independent parameter δ characterises the decay of the connection probabilities of vertices as their distance increases. We prove transience of the infinite cluster in the entire supercritical phase in regimes given by the parameters γ and δ, and complement these results by recurrence results if d=2. Our results are particularly interesting for the soft Boolean graph model discussed in the preprint [arXiv:2108:11252] and the age-dependent random connection model recently introduced by Gracar et al. [Queueing Syst. 93.3-4 (2019)]
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This item is protected by copyright. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Boolean model, preferential attachment, random-connection model, recurrence, Scale-free percolation, transience |
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 09:03 |
Last Modified: | 02 Jun 2023 09:03 |
Status: | Published |
Publisher: | Institute of Mathematical Statistics |
Identification Number: | 10.1214/22-ejp748 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:199851 |