Integrable Systems and Random Matrix Theory Seminar

The height fluctuations of the models in the KPZ class are expected to converge to a universal process. The spatial process at an equal time is known to converge to the Airy process or its variations. However, the temporal process, or more generally the two-dimensional space-time fluctuation field, is less well understood. We consider this question for the periodic TASEP (totally asymmetric simple exclusion process). We evaluate the multi-time and multi-location distribution explicitly in terms of a multiple-integral involving a Fredholm determinant. With some assumptions on the initial condition, we evaluate the large time limit in the so-called relaxation time scale. This is joint with Jinho Baik. Speaker(s): Zhipeng Liu (University of Kansas)