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

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.

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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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Correspondence to Van Hao Can.

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Can, V.H. Exponential Extinction Time of the Contact Process on Rank-One Inhomogeneous Random Graphs. J Theor Probab 32, 106–130 (2019). https://doi.org/10.1007/s10959-017-0786-9

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Keywords

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

Mathematics Subject Classification (2010)

  • 82C22
  • 05C80