KPZ equation from open ASEP with general boundary asymmetry

TL;DR

This paper demonstrates that generalized open ASEP models with boundary-dependent reservoir dynamics converge to the open KPZ equation, broadening the understanding of their continuum limits and removing previous restrictive assumptions.

Contribution

It establishes the continuum limit of generalized open ASEP models to the open KPZ equation without requiring Liggett's condition or product invariant measures.

Findings

Height functions converge to open KPZ equation

Stationary measures converge to those of open KPZ

Removes previous assumptions in the literature

Abstract

We consider generalizations of open ASEP in the interval and half-space, where the speed of the reservoir dynamics can depend on the local particle configuration. We show that their height functions have a continuum limit given by the open KPZ equation. This removes the assumption of Liggett's condition in Corwin-Shen '18 and Parekh '19, thus answering a question of Corwin '22 and Himwich '25, and it removes the assumption of product invariant measures in Goncalves-Perkowski-Simon '20. In the case of the interval, we also show convergence of the stationary measure for the height function increment process to that of the increment process for the open KPZ equation.