Central Limit Theorem for the Contact Process

Abstract

If $(\xi^A(t), t \geq 0)$ is the contact process with initial configuration $A, f: \mathscr{P}(\mathbb{Z}) \rightarrow \mathbb{R}$ is any cylindrical function and $|A| = \infty$, we prove a central limit theorem for $(f(\xi^A(t)), t \geq 0)$ when the rate of infection is supercritical.