LA Probability Forum

UCLA , Math Sciences Bldg., Room 6627

The Kardar-Parisi-Zhang (KPZ) universality class of models is characterized by non Gaussian asymptotic fluctuations coming from random matrices. In this talk, I will define the stochastic six vertex model, a specialization of the classical six vertex model (S6V) which is known to lie in the KPZ class. This model can be viewed as a discrete time version of the asymmetric simple exclusion process. Indeed, it converges to ASEP under a certain limit.

I will explain how, using an idea of Emrah-Janjigian-Seppalainen, one derives the analogue of a formula due to Rains in the context of Last Passage Percolation for the height function of the S6V.  I will then deduce several results on fluctuations, including upper tail bounds for the height function and location of a second-class particle in ASEP, from this formula and coupling arguments.

Joint work with Benjamin Landon.