Asymptotic behaviour of the critical value for the contact process with rapid stirring

We study the behaviour of the contact process with rapid stirring on the lattice ${\mathbb{Z}}^d$ in dimensions $d\ge 3$. This process was studied earlier by Konno and Katori, who proved results for the speed of convergence of the critical value as the rate of stirring approaches infinity. %Katori has improved the result of Katori in $d\ge 3$ and has produced an interval where the critical value must lie. In this article we improve the results of Konno and Kattori and establish the sharp asymptotics of the critical value in dimensions $d\ge 3$.