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.