Brownianity in KPZ

Abstract: The KPZ universality class is believed to contain a very broad collection of models of stochastic growth. A theme in KPZ that has developed a great deal over the last 15 years, and particularly in recent years, is the presence of Brownian behaviour---the classical kind of universality---in many natural objects. In this talk I will survey some of the results in the zero-temperature setting---concerning objects such as last passage percolation, the Airy_2 process, and the KPZ fixed point---focusing on recent advances in obtaining and applying quantitative process-level Brownian comparisons of the Airy_2 process, as well as connections to the behaviour of geodesics in last passage percolation. Based on joint work with Jacob Calvert, Ivan Corwin, Alan Hammond, and Konstantin Matetski.

mathematical physicsprobability

Audience: researchers in the topic

Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

Video recordings of talks are posted online at www.youtube.com/channel/UC0CXjG-ZSIZHy0S40Px2FEQ .