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Super-exponential extinction time of the contact process on random geometric graphs. (English) Zbl 1391.82037

Summary: In this paper we prove lower and upper bounds for the extinction time of the contact process on random geometric graphs with connection 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.

MSC:

82C22 Interacting particle systems in time-dependent statistical mechanics
05C80 Random graphs (graph-theoretic aspects)
60J75 Jump processes (MSC2010)
92C80 Plant biology
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