# Contact process in a wedge

## TL;DR

This paper proves the survival of the supercritical contact process within wedge-shaped regions and explores its coupling with the unrestricted process, with applications to ecological models.

## Contribution

It demonstrates survival conditions in wedge regions and establishes coupling with the unrestricted process, extending understanding of contact process behavior.

## Key findings

- Supercritical contact process survives in wedge regions.
- Coupling with the unrestricted process occurs when it survives.
- Weak coexistence is possible in a specific ecological model.

## Abstract

We prove that the supercritical one-dimensional contact process survives in certain wedge-like space-time regions, and that when it survives it couples with the unrestricted contact process started from its upper invariant measure. As an application we show that a type of weak coexistence is possible in the nearest-neighbor ``grass-bushes-trees'' successional model introduced in Durrett and Swindle (1991).