Non-equilibrium Fluctuations of the Weakly Asymmetric Normalized Binary Contact Path Process

Abstract

This paper is a further investigation of the problem studied in \cite{xue2020hydrodynamics}, where the authors proved a law of large numbers for the empirical measure of the weakly asymmetric normalized binary contact path process on ${\mathbb{Z}}^d,d\ge 3$, and then conjectured that a central limit theorem should hold under a non-equilibrium initial condition. We prove that the aforesaid conjecture is true when the dimension $d$ of the underlying lattice and the infection rate $\lambda$ of the process are sufficiently large.

References in corpus (2)

• Proofs of the martingale FCLT
• The stochastic heat equation as the limit of a stirring dynamics perturbed by a voter model