Electronic Journal of Probability
- Electron. J. Probab.
- Volume 18 (2013), paper no. 103, 36 pp.
Metastable densities for the contact process on power law random graphs
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.
Electron. J. Probab., Volume 18 (2013), paper no. 103, 36 pp.
Accepted: 3 December 2013
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 82C22: Interacting particle systems [See also 60K35]
This work is licensed under a Creative Commons Attribution 3.0 License.
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