# The quasi-stationary distribution of the subcritical contact process

## TL;DR

This paper proves the uniqueness of the quasi-stationary distribution for the subcritical contact process on integer lattices, highlighting a novel example distinct from other non-coming-down-from-infinity processes.

## Contribution

It establishes the first known example of a process with a unique quasi-stationary distribution that does not come down from infinity.

## Key findings

- Uniqueness of the quasi-stationary distribution for the subcritical contact process.
- Contrasts with other processes like stable queues and Galton-Watson.
- First example of such a process with this property.

## Abstract

We show that the quasi-stationary distribution of the subcritical contact process on $\mathbb{Z}^d$ is unique. This is in contrast with other processes which also do not come down from infinity, like stable queues and Galton-Watson, and it seems to be the first such example.