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


Journal Article

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(log n). These results imply that the process on the r -tree has a first-order phase transition. © 2012 Elsevier B.V. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Chatterjee, S; Durrett, R

Published Date

  • January 1, 2013

Published In

Volume / Issue

  • 123 / 2

Start / End Page

  • 561 - 578

International Standard Serial Number (ISSN)

  • 0304-4149

Digital Object Identifier (DOI)

  • 10.1016/j.spa.2012.10.001

Citation Source

  • Scopus