Li-Cheng Tsai (Stanford University)

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

Abstract: It is conjectured that under weak asymmetry, one-dimensional exclusion processes universally converge to the Kardar-Parisi-Zhang (KPZ) equation. Bertini and Giacomin (1997) prove this convergence for the special case of simple exclusion. In this work we extent it to a class of non-simple exclusion processes with a hopping range of at most 3. This is done by generalizing Gaertner's discrete Cole-Hopf transformation. We identify the main nonlinearity and eliminate it by imposing a gradient type condition. This is joint work with Amir Dembo.