报告题目：RSK dynamics, TASEP, and the KPZ fixed point

报告人：廖羽晨 威斯康星大学麦迪逊分校

报告时间：2023.08.09  09:00-10:00  

地点：二教2104 

摘要：The KPZ fixed point, constructed by Matetski-Quastel-Remenik, is a scaling invariant Markov process that is believed to be the universal scaling limit of a large family of random interface growth models, forming the so-called Kardar-Parisi-Zhang university class. In this talk, I will discuss a new way of exactly solving (a discrete-time version of) the totally asymmetric simple exclusion process, a prototypical discrete model in the KPZ universality class.  It is based on a classical combinatorial bijection known as the Robinson-Schensted-Knuth correspondence and standard non-intersecting path constructions. This allows a more systematic derivation for the transition probability formula compared to the original work of MQR and also leads to natural generalizations with particle and time inhomogeneity. Time permitting I will also discuss how to obtain the KPZ fixed point as a scaling limit of TASEP and possible generalizations when there is spatial or temporal inhomogeneity. The talk is based on joint work with Elia Bisi, Axel Saenz and Nikos Zygouras.