Phase transition of the contact process on random regular graphs

作者：Mourrat Jean Christophe^*; Valesin Daniel

来源：Electronic Journal of Probability, 2016, 21(0): 31.

DOI：10.1214/16-EJP4476

• interacting particle systems
• contact process
• random graph
• configuration model

We consider the contact process with infection rate lambda on a random (d + 1)-regular graph with n vertices, G(n). We study the extinction time tau(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 lambda is smaller or larger than lambda(1) (T-d), the lower critical value for the contact process on the infinite, (d + 1) -regular tree: if lambda < lambda(1) (T-d), tau(Gn) grows logarithmically with n, while if lambda > lambda(1) (T-d), it grows exponentially with n. This result differs from the situation where, instead of G(n), 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.

• 出版日期2016