Additive functionals of exclusion processes from non-equilibrium

TL;DR

This paper investigates the non-equilibrium fluctuations of additive functionals in weakly asymmetric exclusion processes on a one-dimensional torus, demonstrating their convergence to a Gaussian process.

Contribution

It extends existing techniques to analyze the scaling limits of additive functionals in non-equilibrium exclusion processes, showing Gaussian process convergence.

Findings

Non-equilibrium fluctuations converge to a Gaussian process

Methodology builds on and extends previous work by Jara and Menezes

Provides a rigorous framework for analyzing additive functionals in asymmetric exclusion

Abstract

Consider the weakly asymmetric simple exclusion processes on the one-dimensional torus. We study the non-equilibrium fluctuation of a class of additive functionals, and show that its scaling limit is a Gaussian process. The proof is mainly based on the results obtained and techniques developed by Jara and Menezes [Non-equiliburim fluctuations of interacting particle systems, arXiv:1810.09526].