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.

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).