Electronic Journal of Probability

Metastable densities for the contact process on power law random graphs

Thomas Mountford, Daniel Valesin, and Qiang Yao

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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.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 103, 36 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064328

Digital Object Identifier
doi:10.1214/EJP.v18-2512

Mathematical Reviews number (MathSciNet)
MR3145050

Zentralblatt MATH identifier
1281.82018

Subjects
Primary: 82C22: Interacting particle systems [See also 60K35]

Keywords
contact process random graphs

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Mountford, Thomas; Valesin, Daniel; Yao, Qiang. Metastable densities for the contact process on power law random graphs. Electron. J. Probab. 18 (2013), paper no. 103, 36 pp. doi:10.1214/EJP.v18-2512. https://projecteuclid.org/euclid.ejp/1465064328


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