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

TL;DR

This paper investigates the asymptotic behavior of the critical value in the contact process with rapid stirring on high-dimensional lattices, providing sharper asymptotic results than previous studies.

Contribution

It improves upon earlier work by Konno and Katori, establishing precise asymptotics of the critical value for the process in dimensions d ≥ 3.

Findings

Established sharp asymptotics of the critical value

Extended understanding of the process in high dimensions

Refined previous convergence rate results

Abstract

We study the behaviour of the contact process with rapid stirring on the lattice $\Z^d$ in dimensions $d\geq 3$. 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 $d\geq 3$ 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 $d\geq 3$.