### Probability and Combinatorics

Tuesday, February 15, 2022 - 3:30pm

#### Xuan Wu

University of Chicago

Location

University of Pennsylvania

David Rittenhouse Lab 4C8

In this talk, we will discuss the LUE, focusing on the scaling limits. On the hard-edge side, we construct the $\alpha$-Bessel line ensemble for all $\alpha \in \mathbb{N}_0$. This novel Gibbsian line ensemble enjoys the $\alpha$-squared Bessel Gibbs property. Moreover, all $\alpha$-Bessel line ensembles can be naturally coupled together in a Bessel field, which enjoys rich integrable structures. We will also talk about work in progress on the soft-edge side, where we expect to have the Airy field as the scaling limit. This talk is based on joint works with Lucas Benigni, Pei-Ken Hung, and Greg Lawler.