In this talk we survey the weak universality (i.e., convergence to the Kardar–Parisi–Zhang or KPZ equation) of interacting particle systems in the KPZ universality class. Such universality is considerably more accessible when a Hopf–Cole (HC) transformation linearizing the particle system exists. Here we derive such a HC transformation for the Higher Spin Exclusion Process (HSEP), introduced by Corwin and Petrov (2015), and hence for all known integrable models of the KPZ class in 1 + 1 dimensions. We further leverage this result into the weak universality of the HSEP. Next, we consider non-nearest neighbor exclusion processes, where an exact HC transformation is unavailable. We show that, for a subclass of models permitting certain gradient-type conditions, an approximated form of the HC transformation exists, and prove the weak universality of the processes.
This talk is based on joint work with Ivan Corwin and joint work with Amir Dembo.
The Probability Seminars are held in Sequoia Hall, Room 200, at 4:30pm on Mondays. Refreshments are served at 4pm in the Lounge on the first floor.