KPZ fixed point convergence of the ASEP and stochastic six-vertex models

TL;DR

This paper proves that the height functions of the stochastic six-vertex model and ASEP converge to the KPZ fixed point under KPZ scaling, extending previous results for ASEP to more general initial conditions.

Contribution

It establishes the KPZ fixed point convergence for both models under broad initial conditions, generalizing prior ASEP-specific results.

Findings

Height functions converge to KPZ fixed point

Results hold for general initial conditions

Extends previous ASEP convergence results

Abstract

We consider the stochastic six-vertex (S6V) model and asymmetric simple exclusion process (ASEP) under general initial conditions which are bounded below lines of arbitrary slope at $\pm\infty$. We show under Kardar-Parisi-Zhang (KPZ) scaling of time, space, and fluctuations that the height functions of these models converge to the KPZ fixed point. Previously, our results were known in the case of ASEP (for a particular direction in the rarefaction fan) via a comparison approach arXiv:2008.06584.