The KPZ fixed point

Jeremy Quastel, University of Toronto
Fine Hall 214

The KPZ universality class contains one dimensional growth models, directed random polymers, stochastic Hamilton-Jacobi equations (e.g. the eponymous Kardar-Parisi-Zhang equation). It is characterized by unusual scale of fluctuations, some of which, surprisingly, come from random matrix theory, and which are model independent but do depend on the initial data. The physical explanation is that in the space of Markov processes, these models are all being rescaled to a universal fixed point. But this scaling invariant fixed point was completely unknown, even by the physicists, until this year, when we managed to compute it in joint work with Konstantin Matetski and Daniel Remenik. It is a new type of integrable Markov process.  In the talk I will describe it, as well as how it was obtained by solving a special model in the class called TASEP.