# KPZ equation limit of stochastic higher spin six vertex model

## TL;DR

This paper proves that the stochastic higher spin six vertex model converges to the KPZ equation under weak asymmetry for general spin parameters, extending previous results limited to the case I=J=1.

## Contribution

It generalizes the convergence result of the SHS6V model to the KPZ equation from the specific case I=J=1 to arbitrary integer spins I, J.

## Key findings

- Convergence of SHS6V to KPZ under weak asymmetry.
- Extension of previous results to general spins I, J.
- Validation of KPZ universality for broader class of models.

## Abstract

We consider the stochastic higher spin six vertex (SHS6V) model introduced in [Corwin-Petrov, 2016] with general integer spin parameters $I, J$. Starting from near stationary initial condition, we prove that the SHS6V model converges to the KPZ equation under weakly asymmetric scaling. This generalizes the result of [Corwin-Ghosal-Shen-Tsai, 2018] from $I = J =1$ to general $I, J$.