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Percolation phase transition in weight-dependent random connection models

Part of: Graph theory Special processes

Published online by Cambridge University Press:  22 November 2021

Peter Gracar Open the ORCID record for Peter Gracar [Opens in a new window] ,
Lukas Lüchtrath Open the ORCID record for Lukas Lüchtrath [Opens in a new window]  and
Peter Mörters Open the ORCID record for Peter Mörters [Opens in a new window]
Peter Gracar*
Affiliation:
University of Cologne
Lukas Lüchtrath*
Affiliation:
University of Cologne
Peter Mörters*
Affiliation:
University of Cologne
*
*Postal address: Weyertal 86-90, 50931 Köln, Germany.
*Postal address: Weyertal 86-90, 50931 Köln, Germany.
*Postal address: Weyertal 86-90, 50931 Köln, Germany.
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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.

Keywords

Subcritical regimerandom geometric graphBoolean modelscale-free percolationlong-range percolationspatial networkrobustnessage-based spatial preferential attachment

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 05C80: Random graphs
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 4 , December 2021 , pp. 1090 - 1114
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Copyright
© The Author(s) 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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