View abstract

MCA Prize Lecture

Thursday, July 22, 12:15 ~ 13:15 UTC-3

The KPZ fixed point

Daniel Remenik

Universidad de Chile, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The KPZ universality class is a broad collection of probabilistic models including one-dimensional random growth, directed polymers and particle systems. The class is characterized by an unusual and very rich fluctuation behavior, with asymptotic distributions which for some special choices of initial conditions are connected to random matrix theory. The KPZ fixed point is a special, scaling invariant Markov process which arises as the universal scaling limit of all models in the class, and contains all of its fluctuation behavior. In this talk I'm going to introduce this object and describe how it is obtained from certain special models in the class. I will then explain how the KPZ fixed point can be interpreted as a stochastic integrable system and how this leads to a connection with a famous completely integrable dispersive PDE, the Kadomtsev-Petviashvili equation.

Joint work with Konstantin Matetski (Columbia U.) and Jeremy Quastel (U. of Toronto).

View abstract PDF