On the growth of one-dimensional reverse immunization contact processes

TL;DR

This paper studies a modified supercritical contact process with reverse immunization, establishing regeneration points, a strong law, a central limit theorem, and extending convergence results for the process.

Contribution

It introduces a new analysis of a reverse immunization contact process, providing regeneration points and probabilistic limit theorems not previously established.

Findings

Identification of regeneration points for the process

Proof of a strong law of large numbers

Establishment of a central limit theorem

Abstract

We are concerned with the supercritical contact process modified so that first infection occurs at a lower rate, it is known that the process survives with positive probability. Regarding the rightmost infected of the process started from one site infected and conditioned to survive, we specify a sequence of space-time points at which its behaviour regenerates and thus obtain the corresponding strong law and central limit theorem. We also extend complete convergence to this modified case.