Super-exponential extinction time of the contact process on random geometric graphs

Abstract

In this paper, we prove lower and upper bounds for the extinction time of the contact process on random geometric graphs with connecting radius tending to infinity. We obtain that for any infection rate $\lambda >0$, the contact process on these graphs survives a time super-exponential in the number of vertices.

arXiv commentAccepted for publication in Combinatorics, Probability and Computing