Fluctuations of large random systems are believed to exhibit universal pattern. Classical central limit theorem is a typical example where sum of i.i.d. random variables always converge to Gaussian distribution after proper renormalization. In this talk I will discuss some other universality classes beyond classical central limit theorem. I will mainly focus on the so-called Kardar-Parisi-Zhang (KPZ) universality class which includes models from random interface growth, interacting particle systems, random matrices, random tilings and so on. After a brief overview of several models in the KPZ class, I will discuss in detail one particular model, the totally asymmetric simple exclusion process (TASEP) which is a famous interacting particle system modeling traffic flows. I will derive exact formula for the transition probability of TASEP using the so-called Bethe ansatz coming from quantum integrable systems. Time permits, I will discuss one-point distribution and asymptotics as well.
Speaker(s): Yuchen Liao (University of Michigan)