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

TL;DR

This paper establishes two limit theorems for the high-dimensional two-stage contact process, analyzing its invariant measure and critical value as the lattice dimension increases, extending classical results for basic contact processes.

Contribution

It introduces two limit theorems for the high-dimensional two-stage contact process, expanding understanding of its asymptotic behavior and critical parameters.

Findings

Upper invariant measure converges as dimension grows.

Critical value exhibits specific asymptotic behavior.

Results extend classical contact process theorems.

Abstract

In this paper we are concerned with the two-stage contact process introduced in \cite{Krone1999} 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 measure 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 in \cite{Grif1983} and \cite{Schonmann1986}.