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2013 Metastable densities for the contact process on power law random graphs
Thomas Mountford, Daniel Valesin, Qiang Yao
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Electron. J. Probab. 18: 1-36 (2013). DOI: 10.1214/EJP.v18-2512

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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Thomas Mountford. Daniel Valesin. Qiang Yao. "Metastable densities for the contact process on power law random graphs." Electron. J. Probab. 18 1 - 36, 2013. https://doi.org/10.1214/EJP.v18-2512

Information

Accepted: 3 December 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1281.82018
MathSciNet: MR3145050
Digital Object Identifier: 10.1214/EJP.v18-2512

Subjects:
Primary: 82C22

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