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October 2019 Metastability of the contact process on fast evolving scale-free networks
Emmanuel Jacob, Amitai Linker, Peter Mörters
Ann. Appl. Probab. 29(5): 2654-2699 (October 2019). DOI: 10.1214/18-AAP1460

Abstract

We study the contact process in the regime of small infection rates on finite scale-free networks with stationary dynamics based on simultaneous updating of all connections of a vertex. We allow the update rates of individual vertices to increase with the strength of a vertex, leading to a fast evolution of the network. We first develop an approach for inhomogeneous networks with general kernel and then focus on two canonical cases, the factor kernel and the preferential attachment kernel. For these specific networks, we identify and analyse four possible strategies how the infection can survive for a long time. We show that there is fast extinction of the infection when neither of the strategies is successful, otherwise there is slow extinction and the most successful strategy determines the asymptotics of the metastable density as the infection rate goes to zero. We identify the domains in which these strategies dominate in terms of phase diagrams for the exponent describing the decay of the metastable density.

Citation

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Emmanuel Jacob. Amitai Linker. Peter Mörters. "Metastability of the contact process on fast evolving scale-free networks." Ann. Appl. Probab. 29 (5) 2654 - 2699, October 2019. https://doi.org/10.1214/18-AAP1460

Information

Received: 1 July 2018; Published: October 2019
First available in Project Euclid: 18 October 2019

zbMATH: 07155056
MathSciNet: MR4019872
Digital Object Identifier: 10.1214/18-AAP1460

Subjects:
Primary: 05C82
Secondary: 82C22

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 5 • October 2019
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