Scaling limit of subcritical contact process

TL;DR

This paper analyzes the behavior of the subcritical contact process on a lattice over large times, characterizing the macroscopic infected regions and their internal structure.

Contribution

It provides a detailed description of the large-time scaling limit of the subcritical contact process starting from full infection.

Findings

Characterization of infected regions at large times

Description of relative positions within infected regions

Insights into the spatial structure of the process

Abstract

In this paper we describe the subcritical contact process on $\Z^d$ for large times, starting with all sites infected. The configuration is described in terms of the macroscopic locations of infected regions in space and the relative positions of infected sites in each such region.