Graph Constructions for the Contact Process with a Prescribed Critical Rate

Stein Andreas Bethuelsen, Gabriel Baptista Silva () and Daniel Valesin
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Stein Andreas Bethuelsen: University of Bergen
Gabriel Baptista Silva: University of Groningen
Daniel Valesin: University of Groningen

Journal of Theoretical Probability, 2022, vol. 35, issue 2, 863-893

Abstract: 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).

Keywords: Contact process; Phase transition; Interacting particle systems; Critical value; 82C22; 60K35 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-020-01063-4

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