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The contact process on scale-free geometric random graphs

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  • Gracar, Peter
  • Grauer, Arne

Abstract

We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on Rd. This class includes the age-dependent random connection model and the soft Boolean model. In the ultrasmall regime of these random graphs we provide exact asymptotics for the non-extinction probability when the rate of infection spread is small and show for a finite version of these graphs that the extinction time is of exponential order in the size of the graph.

Suggested Citation

  • Gracar, Peter & Grauer, Arne, 2024. "The contact process on scale-free geometric random graphs," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:spapps:v:173:y:2024:i:c:s0304414924000668
    DOI: 10.1016/j.spa.2024.104360
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    References listed on IDEAS

    as
    1. Mountford, Thomas & Mourrat, Jean-Christophe & Valesin, Daniel & Yao, Qiang, 2016. "Exponential extinction time of the contact process on finite graphs," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 1974-2013.
    2. Peter Gracar & Arne Grauer & Lukas Lüchtrath & Peter Mörters, 2019. "The age-dependent random connection model," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 309-331, December.
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