Weakly Asymmetric Non-Simple Exclusion Process and the Kardar-Parisi-Zhang Equation

Understand

We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing Gaertners Cole-Hopf transformation.

• We identify the main non-linearity and eliminate it by imposing a gradient type condition.
• For hopping range at most 3, using the generalized transformation, we prove the convergence of the exclusion process toward the Kardar-Parisi-Zhang (KPZ) equation.
• This is the first universality result concerning interacting particle systems in the context of KPZ universality class.