Continuity of the asymptotic shape of the supercritical contact process

TL;DR

This paper proves that the asymptotic growth shape of the supercritical contact process in Z^d varies continuously with the infection parameter, establishing a fundamental property of the process in any dimension.

Contribution

It establishes the continuity of the asymptotic shape of the supercritical contact process with respect to the infection parameter across all dimensions.

Findings

Continuity of the asymptotic shape in the supercritical contact process.

Valid in all dimensions d ≥ 1.

Provides a rigorous proof of shape stability with parameter changes.

Abstract

We prove the continuity of the shape governing the asymptotic growth of the supercritical contact process in Z^d , with respect to the infection parameter. The proof is valid in any dimension d $\ge$ 1.