An improved upper bound for the critical value of the contact process on $\mathbb{Z} ^d$ with $d\geq 3$

Abstract

By coupling the basic contact process with a linear system, we give an improved upper bound for the critical value $\lambda _c$ of the basic contact process on the lattice $\mathbb{Z} ^d$ with $d\geq 3$. As a direct corollary of our result, the critical value of the three-dimensional contact process is shown to be at most $0.34$.