Subcritical Contact Process Seen from the Edge: Convergence to Quasi-Equilibrium

TL;DR

This paper studies the subcritical contact process from the perspective of the rightmost infected site, proving it converges to a quasi-stationary measure despite lacking invariant measures.

Contribution

It establishes the convergence to a quasi-stationary measure for the subcritical contact process viewed from the edge, a novel perspective in the study of such processes.

Findings

Convergence in distribution to a quasi-stationary measure.

Absence of invariant measures for the process from the edge.

Support on finite configurations.

Abstract

The subcritical contact process seen from the rightmost infected site has no invariant measures. We prove that nevertheless it converges in distribution to a quasi-stationary measure supported on finite configurations.