The contact process on scale-free geometric random graphs

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.

28 pages, 3 figures

References in corpus (2)

• Recurrence versus Transience for Weight-Dependent Random Connection Models
• The contact process on random hyperbolic graphs: metastability and critical exponents