CLT for NESS of a reaction-diffusion model

TL;DR

This paper investigates the scaling behavior of non-equilibrium stationary states in a reaction-diffusion model, establishing laws of large numbers, local equilibrium approximations, and a central limit theorem with Gaussian limits.

Contribution

It provides the first CLT for the particle density in NESS of a reaction-diffusion model, including explicit convergence rates and Gaussian field representations.

Findings

Law of large numbers for particle density in NESS

Approximation of NESS by local equilibrium measures

Central limit theorem with Gaussian limits in dimensions d ≤ 3

Abstract

We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the NESS, with an explicit rate of convergence, and we also show that at mesoscopic scales the NESS is well approximated by a local equilibrium (product) measure, in the total variation distance. In addition, in dimensions $d \leq3$ we show a central limit theorem (CLT) for the density of particles under the NESS. The corresponding Gaussian limit can be represented as an independent sum of a white noise and a massive Gaussian free field, and in particular it presents macroscopic correlations.