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

TL;DR

This paper investigates the metastability of the contact process on random regular graphs, demonstrating exponential growth of extinction time and convergence to an exponential distribution, revealing key dynamical properties.

Contribution

It provides a new theoretical result on the exponential growth and distributional convergence of extinction times in the contact process on random regular graphs.

Findings

Extinction time grows exponentially with the number of vertices.

Extinction time divided by its mean converges to a unit exponential distribution.

The results characterize the metastable behavior of the process.

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.