Local KPZ Behavior Under Arbitrary Scaling Limits

One of the main difficulties in proving convergence discrete models surface growth to Kardar-Parisi-Zhang (KPZ) equation dimensions higher than one is that correct way take a scaling limit, so limit nontrivial, not known rigorous sense. To understand KPZ without being hindered by this issue, article introduces notion "local behavior", which roughly means instantaneous at point decomposes into sum Laplacian term, gradient squared noise term behaves like white noise, and remainder negligible compared other three terms their sum. The result for general class surfaces, contains model directed polymers random environment as special case, local behavior occurs under arbitrary limits, any dimension.