The contact process with aging

TL;DR

This paper introduces a contact process with aging, where particle age affects reproduction, and proves a shape theorem using coupling with percolation, extending to the two-stage contact process.

Contribution

It generalizes the classical contact process by incorporating aging and adapts existing methods to prove new shape theorems.

Findings

Shape theorem for the aging contact process

Coupling with supercritical oriented percolation

Results applicable to the two-stage contact process

Abstract

In this article, we introduce a contact process with aging: in this generalization of the classical contact process, each particle has an integer age that influences its ability to give birth. We prove here a shape theorem for this process conditioned to survive. In order to establish some key exponential decays, we adapt the Bezuidenhout and Grimmett construction [BG91] to build a coupling between our process and a supercritical oriented percolation. Our results also apply to the two-stage contact process introduced by Krone [Kro92].