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Journal of Theoretical Probability

, Volume 32, Issue 1, pp 106–130 | Cite as

Exponential Extinction Time of the Contact Process on Rank-One Inhomogeneous Random Graphs

  • Van Hao CanEmail author
Article
First Online:
  • 75 Downloads

Abstract

We show that the contact process on the rank-one inhomogeneous random graphs and Erdos–Rényi graphs with mean degree large enough survives a time exponential in the size of these graphs for any positive infection rate. In addition, a metastable result for the extinction time is also proved.

Keywords

Contact process Inhomogeneous random graphs Erdos–Rényi random graphs Extinction time 

Mathematics Subject Classification (2010)

82C22 05C80 
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Notes

Acknowledgements

I am grateful to Bruno Schapira for his help and suggestions during the preparation of this work. I wish to thank also the anonymous referee for carefully reading the manuscript and many valuable comments. This work is supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 101.03–2017.07.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.CNRS, Centrale Marseille, I2M, UMR 7373Aix Marseille UniversitéMarseilleFrance
  2. 2.Institute of MathematicsVietnam Academy of Science and TechnologyHa NoiViet Nam

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