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Math Colloquium
Timo Seppalainen University of Wisconsin-Madison Title: Exclusion and zero-range processes: Stochastic models of interacting particles Abstract: This talk is an introduction to the two most-studied asymmetric conservative stochastic particle systems on the integer lattice, namely exclusion and zero-range processes. After an introduction to TASEP, the totally asymmetric simple exclusion process, we prove a hydrodynamic limit for a generalization that admits K particles per site. This limit is a law of large numbers at the level of the space-time evolution of the process. It shows that macroscopically the motion of particles is governed by a PDE of the scalar conservation law type with a concave flux function. From laws of large numbers we move to fluctuations to discuss the fluctuation exponent for the current of a class of zero-range processes (ZRP). This is presently the only precise result on Kardar-Parisi-Zhang exponents that goes beyond known integrable models. The last topic is on the special case of ZRP where particles move independently. Fluctuations do not obey KPZ universality but instead another behavior called Edwards-Wilkinson universality. Date: Wednesday, February 24, 2016Time: 4:30 pmLocation: Wean Hall 7500Submitted by: BohmanNote: Refreshments at 4:00 pm, Wean Hall 6220 |