## Electronic Journal of Probability

### Metastability for the contact process on the configuration model with infinite mean degree

#### Abstract

We study the contact process on the configuration model with a power law degree distribution, when the exponent is smaller than or equal to two.

We prove that the extinction time grows exponentially fast with the size of the graph and prove two metastability results. First the extinction time divided by its mean converges in distribution toward

an exponential random variable with mean one, when the size of the graph tends to infinity. Moreover, the density of infected sites taken at exponential times converges in probability to a constant. This extends previous results in the case of an exponent larger than $2$ obtained previously.

#### Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 26, 22 pp.

Dates
Accepted: 9 March 2015
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465067132

Digital Object Identifier
doi:10.1214/EJP.v20-3859

Mathematical Reviews number (MathSciNet)
MR3325096

Zentralblatt MATH identifier
1327.82051

Rights

#### Citation

Can, Van Hao; Schapira, Bruno. Metastability for the contact process on the configuration model with infinite mean degree. Electron. J. Probab. 20 (2015), paper no. 26, 22 pp. doi:10.1214/EJP.v20-3859. https://projecteuclid.org/euclid.ejp/1465067132

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