The Complete Convergence Theorem Holds for Contact Processes in a Random Environment on $Z^d\times Z^+$

TL;DR

This paper proves that the complete convergence theorem applies to contact processes in a static random environment on half-space lattices, extending classical results to more complex, randomized settings.

Contribution

It generalizes the complete convergence theorem to contact processes in static random environments on half-space lattices, a significant extension of prior classical results.

Findings

The complete convergence theorem holds for almost every environment.

The result applies to contact processes with i.i.d. infection rates and constant recovery rates.

It extends classical contact process results to random environments.

Abstract

In this article, we consider the basic contact process in a static random environment on the half space $Z^d\times Z^+$ where the recovery rates are constants and the infection rates are independent and identically distributed random variables. We show that, for almost every environment, the complete convergence theorem holds. This is a generalization of the known result for the classical contact process in the half space case.