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Graph Constructions for the Contact Process with a Prescribed Critical Rate

Author

Listed:
  • Stein Andreas Bethuelsen

    (University of Bergen)

  • Gabriel Baptista Silva

    (University of Groningen)

  • Daniel Valesin

    (University of Groningen)

Abstract

We construct graphs (trees of bounded degree) on which the contact process has critical rate (which will be the same for both global and local survival) equal to any prescribed value between zero and $$\lambda _c({\mathbb {Z}})$$ λ c ( Z ) , the critical rate of the one-dimensional contact process. We exhibit both graphs in which the process at this target critical value survives (locally) and graphs where it dies out (globally).

Suggested Citation

  • Stein Andreas Bethuelsen & Gabriel Baptista Silva & Daniel Valesin, 2022. "Graph Constructions for the Contact Process with a Prescribed Critical Rate," Journal of Theoretical Probability, Springer, vol. 35(2), pages 863-893, June.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:2:d:10.1007_s10959-020-01063-4
    DOI: 10.1007/s10959-020-01063-4
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    References listed on IDEAS

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    1. Mountford, Thomas & Mourrat, Jean-Christophe & Valesin, Daniel & Yao, Qiang, 2016. "Exponential extinction time of the contact process on finite graphs," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 1974-2013.
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