The KPZ fixed point

Speaker: Jeremy Quastel

Date: Fri, Oct 19, 2018 to Sat, Oct 20, 2018

Location: PIMS, University of British Columbia

Conference: CRM-Fields-PIMS Prize Lecture

Subject: Mathematics

Class: Scientific


The (1d) KPZ universality class contains random 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 appeared earlier in random matrix theory, and which depend on the initial data. The explanation is that on large scales everything approaches a special scaling invariant Markov process, the KPZ fixed point. It is obtained by solving one model in the class, TASEP, and passing to the limit. Both TASEP and the KPZ fixed point turn out to have a novel structure: "stochastic integrable systems" (Joint work with Konstantin Matetski and Daniel Remenik).