Metastable densities for the contact process on power law random graphs
Daniel Valesin (University of British Columbia)
Qiang Yao (East China Normal University)
Abstract
We consider the contact process on a random graph with fixed degree distribution given by a power law. We follow the work of Chatterjee and Durrett (2009), who showed that for arbitrarily small infection parameter $\lambda$, the survival time of the process is larger than a stretched exponential function of the number of vertices, $n$. We obtain sharp bounds for the typical density of infected sites in the graph, as $\lambda$ is kept fixed and $n$ tends to infinity. We exhibit three different regimes for this density, depending on the tail of the degree law.
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Pages: 1-36
Publication Date: December 3, 2013
DOI: 10.1214/EJP.v18-2512
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