Non-equilibrium fluctuations of the weakly asymmetric normalized binary contact path process

Abstract

This paper is a further investigation of the problem studied in Xue and Zhao (2020), where the authors proved a law of large numbers for the empirical measure of the weakly asymmetric normalized binary contact path process on Zd,d≥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 λ of the process are sufficiently large.