Probability and Mathematical Physics Seminar
Multi-time distribution of TASEP
Speaker: Zhipeng Liu, University of Kansas
Location: Warren Weaver Hall 1302
Friday, March 13, 2020, noon CANCELLED
The Totally Asymmetric Simple Exclusion Process (TASEP) is the most studied model in the Kardar-Parisi-Zhang (KPZ) university class. The one point limiting distributions are the well-known Tracy-Widom distributions and their analogs, and the spatial processes are the so-called Airy processes. However, along the temporal direction much less is known until very recently. In this talk, we will first review some recent progresses along this direction, then discuss a novel formula of the finite time multi-point distribution formula of TASEP in the space-time plane. This formula is in terms of multiple contour integrals of a Fredholm determinant, with initial conditions encoded in a symmetric polynomial, which is related to the dual Grothendieck polynomial and the inhomogeneous Schur polynomials. We are also able to find the limits of this multi-point distribution formula for both step and flat initial conditions when the times are different and go to infinity proportionally. These limits are believed to be universal, and hence are expected to be the limiting multi-time distributions for all the models in the KPZ universality class (with step or flat initial conditions).