The Kardar-Parisi-Zhang (KPZ) equation is a conjecturally universal model for dynamics of fluctuating interfaces such as fires and epidemic fronts. The universality was originally justified by Kardar, Parisi, and Zhang via non-rigorous renormalization group calculations. In this talk, we introduce some mathematically rigorous results and take a step towards this universality in the context of some non-integrable interacting particle systems outside their respective invariant measures.

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