KPZ equation from ASEP plus general speed-change drift

TL;DR

This paper derives the KPZ equation as a continuum limit from ASEP with configuration-dependent drift, providing a novel approach without relying on duality or explicit invariant measures.

Contribution

It introduces new estimates on Kolmogorov equations to establish the KPZ limit for a broad class of particle systems, expanding the theoretical framework.

Findings

KPZ equation derived from ASEP with general drift

New estimates on Kolmogorov equations developed

Robust proof of the Boltzmann-Gibbs principle

Abstract

We derive the KPZ equation as a continuum limit of height functions in asymmetric simple exclusion processes with drift that depends on the local particle configuration. To our knowledge, it is a first such result for a class of particle systems without duality or explicit invariant measures. The tools developed in this paper consist of estimates on the corresponding Kolmogorov equations, giving a more robust proof of the Boltzmann-Gibbs principle. These tools are not exclusive to KPZ.