# Thorsten Neuschel: Critical behavior of non-intersecting Brownian motions

**Time: **
Thu 2019-10-17 15.15 - 16.15

**Lecturer: **
Thorsten Neuschel

**Location: **
F11, KTH

### Abstract

We study the local behavior of the eigenvalue processes of Hermitian Brownian motions (Dyson Brownian motion) for large dimensions. These random eigenvalues form a determinantal point process for which in non-critical situations it is known that the local correlations show sine-kernel universality in the bulk of the spectrum whereas Airy-type correlations are found at the edge of spectral gaps on a macroscopic scale. In this talk we focus on certain naturally arising critical situations leading to gaps of mesoscopic size. We show that the corresponding multi-time correlations locally exhibit Airy- or Pearcey-kernel universality even in the case of interior points of the support of the spectral limit. The results presented are based on joint work with Tom Claeys and Martin Venker and they are part of a project which is still in progress.