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2015 Metastability for the contact process on the configuration model with infinite mean degree
Van Hao Can, Bruno Schapira
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Electron. J. Probab. 20: 1-22 (2015). DOI: 10.1214/EJP.v20-3859

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.

Citation

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Van Hao Can. Bruno Schapira. "Metastability for the contact process on the configuration model with infinite mean degree." Electron. J. Probab. 20 1 - 22, 2015. https://doi.org/10.1214/EJP.v20-3859

Information

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

zbMATH: 1327.82051
MathSciNet: MR3325096
Digital Object Identifier: 10.1214/EJP.v20-3859

Subjects:
Primary: 82C22
Secondary: 05C80, 60K35

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