KPZ Limit Theorems

Explore a 46-minute lecture on KPZ limit theorems presented by Jinho Baik at the International Mathematical Union. Delve into one-dimensional interacting particle systems, 1+1 random growth models, and two-dimensional directed polymers that define two-dimensional random fields. Learn about the KPZ universality conjecture, which proposes that appropriately scaled height functions converge to a model-independent universal random field for various models. Examine limit theorems and their variations across different domains, with a focus on recent findings in periodic domains. Gain insights into integrable probability models, integrable differential equations, and universality. The lecture covers topics such as directed last passage percolations, the corner growth model, TASEP, integrable methods, and relaxation time limits for periodic corner growth models. Discover how to solve the Kolmogorov forward equation on the line and understand transition probabilities for periodic TASEP. Access accompanying slides for visual support of the concepts presented.