Phase transition of the contact process on random regular graphs

Jean Christophe Mourrat, Daniel Valesin

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the contact process with infection rate λ on a random (d + 1)-regular graph with n vertices, Gn. We study the extinction time τGn (that is, the random amount of time until the infection disappears) as n is taken to infinity. We establish a phase transition depending on whether λ is smaller or larger than λ1((image found)d), the lower critical value for the contact process on the infinite, (d+1)-regular tree: if λ < λ1((image found)d), τGn grows logarithmically with n, while if λ > λ1((image found)d), it grows exponentially with n. This result differs from the situation where, instead of Gn, the contact process is considered on the d-ary tree of finite height, since in this case, the transition is known to happen instead at the upper critical value for the contact process on Td.

Original languageEnglish (US)
JournalElectronic Journal of Probability
Volume21
DOIs
StatePublished - 2016

Keywords

  • Configuration model
  • Contact process
  • Interacting particle systems
  • Random graph

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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