The KPZ Fixed Point - Understanding Random Growing Interfaces

Explore the KPZ universality class and its fixed point in this 51-minute lecture by Konstantin Matetski at ICBS2024. Delve into mathematical models describing random growing interfaces, including exclusion processes, last-passage percolations, and directed polymers in random environments. Discover how the KPZ fixed point emerges as the universal scaling limit for all models within this class. Examine the connection between the KPZ fixed point's marginal distributions and Tracy-Widom distributions from random matrix theory for specific initial states. Learn about the complete characterization of the KPZ fixed point as a scaling limit of the totally asymmetric simple exclusion process, developed by Matetski, Quastel, and Remenik. Investigate the application of their solution method to various models in the universality class, revealing intriguing relationships with classic integrable systems such as the Toda lattice and the Kadomtsev-Petviashvili equation.