Caltech-Tsinghua Joint Colloquium

https://caltech.zoom.us/j/83185685455

A cornerstone of modern probability theory is the Central Limit Theorem, which states that the normal distribution (and, in a dynamic setting, Brownian motion) serves as the universal scaling limit for a broad class of random models, with numerous applications across science and engineering.

Over the past few decades, a new universality class—named after Kardar, Parisi, and Zhang (KPZ)—has emerged to describe another range of physical and probabilistic models, including growth processes, interacting particle systems, and random matrix models. While the analog of the Central Limit Theorem—the strong KPZ universality conjecture—remains open, key limiting processes, such as the KPZ fixed point and the directed landscape, have been constructed in recent years, with many properties (such as distribution functions) now understood. I will introduce these processes, and present recent progress (joint with Dauvergne) toward developing a unified limiting theory.