## Electronic Journal of Probability

### Metastable densities for the contact process on power law random graphs

#### 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

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

Keywords
contact process random graphs

Rights

#### 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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