Speaker : | Mr. Li-Cheng Tsai (Stanford University) |
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Title : | Weakly Asymmetric Non-Simple Exclusion Process and the Kardar-Parisi-Zhang Equation |
Time : | 2014-09-15 (Mon) 14:10 - |
Place : | Seminar Room 617, Institute of Mathematics (NTU Campus) |
Abstract: | It is conjectured that under weak asymmetry, one-dimensional exclusion processes universally converge to the Kardar-Parisi-Zhang (KPZ) equation. Based on Gaertner's discrete Cole-Hopf transformation, Bertini and Giacomin (1997) prove this convergence for the special case of simple (nearest-neighbor) exclusion. In this work we extend the discrete Cole-Hopf transformation, and eliminate the main nonlinearity using a gradient-type condition. We thus obtain the universal convergence to the KPZ equation of a class of non-simple exclusion processes with a hopping range of at most 3. This is joint work with Amir Dembo. |