We prove that under a particular weak scaling, the 4-parameter interacting particle system introduced by Corwin and Petrov [Comm. Math. Phys. 343 (2016) 651–700] converges to the Kardar–Parisi–Zhang (KPZ) equation. This expands the relatively small number of systems for which weak universality of the KPZ equation has been demonstrated.
"KPZ equation limit of higher-spin exclusion processes." Ann. Probab. 45 (3) 1771 - 1798, May 2017. https://doi.org/10.1214/16-AOP1101