The contact process on finite homogeneous trees revisited

Abstract

We consider the contact process with infection rate on T d , the d-ary tree of height n. We study the extinction time Td , that is, the random time it takes for the infection to disappear when the process is started from full occupancy. We prove two conjectures of Stacey regarding Td . Let 2 denote the upper critical value for the contact process on the innite d-ary tree. First, if