Non-stationary KPZ equation from ASEP with slow bonds

We prove the height functions for a class of non-integrable and non-stationary particle systems converge to the KPZ equation, thereby making progress on the universality of the KPZ equation. The models herein are ASEP (Comm. Math. Phys. 183 (1997) 571-606) with a mesoscopic family of slow bonds, thus we partially extend (Comm. Math. Phys. 346 (2016) 801-838) to non-stationary models and add to the almost empty set of non-integrable, non-stationary interacting particle systems for which universality is established. To do this, we develop further the strategy of (Yang (2020); Probab. Theory Related Fields 183 (2022) 415-545) introduce a method to establish a novel principle that builds upon the classical hydrodynamic limits of (Comm. Math. Phys. 118 (1988) 31-59) and that we call local hydrodynamics.