Two limit theorems for the high-dimensional two-stage contact process

Abstract

In this paper we are concerned with the two-stage contact process introduced by Krone (1999) on a high-dimensional lattice. By comparing this process with an auxiliary model which is a linear system, we obtain two limit theorems for this process as the dimension of the lattice grows to infinity. The first theorem is about the upper invariant law of the process. The second theorem is about asymptotic behavior of the critical value of the process. These two theorems can be considered as extensions of their counterparts for the basic contact processes proved by Griffeath (1983) and Schonmann and Vares (1986).