A Metastability Result for the Contact Process on a Random Regular Graph

2015/03/17 by Su, Wei
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1503.04895

Abstract

In this paper we study the metastability of the contact process on a random regular graph. We show that the extinction time of the contact process, when initialized so that all vertices are infected at time 0, grows exponentially with the vertex number. Moreover, we show that the extinction time divided by its mean converges to a unit exponential distribution in law.

Related

• Explicit bounds for critical infection rates and expected extinction times of the contact process on finite random graphs
• Metastability for the contact process on the configuration model with infinite mean degree
• Metastable Densities for Contact Processes on Power Law Random Graphs
• Exponential extinction time of the contact process on rank-one inhomogeneous random graphs
• Phase transition of the contact process on random regular graphs