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A first order phase transition in the threshold θ≥2 contact process on random r-regular graphs and r-trees

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  • Chatterjee, Shirshendu
  • Durrett, Rick
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    Abstract

    We consider the discrete time threshold-θ contact process on a random r-regular graph. We show that if θ≥2, r≥θ+2, ϵ1 is small and p≥p1(ϵ1), then starting from all vertices occupied the fraction of occupied vertices is ≥1−2ϵ1 up to time exp(γ1(r)n) with high probability. We also show that for p2<1 there is an ϵ2(p2)>0 so that if p≤p2 and the initial density is ≤ϵ2(p2), then the process dies out in time O(logn). These results imply that the process on the r-tree has a first-order phase transition.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 123 (2013)
    Issue (Month): 2 ()
    Pages: 561-578

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    Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:561-578

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    Related research

    Keywords: Threshold contact process; Random regular graphs; Isoperimetric inequality; First order phase transition; Binomial large deviations;

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