The contact process on scale-free geometric random graphs

Peter Gracar; Arne Grauer

doi:10.1016/j.spa.2024.104360

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arXiv · 2208.08346

The contact process on scale-free geometric random graphs

Peter Gracar·Arne Grauer

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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 $\mathbb{R}^d$. 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.

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Peter Gracar, Arne Grauer. 2022-08-17. The contact process on scale-free geometric random graphs. https://doi.org/10.1016/j.spa.2024.104360

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