Gibbsian Line Ensembles: A Marriage of Integrability and Probability

The Department of Mathematics in the College of Arts and Sciences is honored to welcome Dr. Xuan Wu to deliver the weekly colloquium. Dr. Wu is a Dickson Instructor in the Mathematics Department, University of Chicago, where she works in probability, stochastic PDEs, and random operators, particularly the asymptotic analysis of stochastic integrable systems at the interface of random matrix theory, stochastic PDEs, and statistical physics.

Abstract: Many important models in integrable probability, for example, the famous KPZ equation, can be embedded into Gibbsian line ensembles. The Gibbs property provides a powerful resampling invariance against Brownian bridges over an arbitrary interval. In this talk, Wu will explain the origin and applications of this hidden probabilistic structure using the KPZ line ensemble as an example.