Phase transition of the contact process on random regular graphs

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 τ Gn (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 λ 1 (T d), the lower critical value for the contact process on the infinite, (d + 1)-regular tree: if λ < λ 1 (T d), τ Gn grows logarithmically with n, while if λ > λ 1 (T 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 T d.
Document type :
Journal articles
Complete list of metadatas

Cited literature [21 references]  Display  Hide  Download

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01401885
Contributor : Jean-Christophe Mourrat <>
Submitted on : Wednesday, November 23, 2016 - 10:16:57 PM
Last modification on : Thursday, January 11, 2018 - 6:12:31 AM
Long-term archiving on : Monday, March 27, 2017 - 4:20:22 AM

Files

contact_reg.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Jean-Christophe Mourrat, Daniel Valesin. Phase transition of the contact process on random regular graphs. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2016, 21, ⟨10.1214/16-EJP4476⟩. ⟨ensl-01401885⟩

Share

Metrics

Record views

90

Files downloads

139