A&Q seminar with Martin Venker
Title: Critical Correlations of Non-Intersecting Brownian Motions: Airy, Pearcey, and an interpolation
Speaker: Martin Venker
Abstract: Non-Intersecting Brownian Motions constitute the most accessible dynamical model in random matrix theory, describing the eigenvalues of a Brownian motion in the space of Hermitian matrices. It is the dynamical counterpart of the famous Gaussian Unitary Ensemble but is mathematically much richer as it allows to study e.g. the merging of two initially separated bulks of eigenvalues at some critical time. In this talk we will see a very general, but mathematically remarkably simple, classification of universal processes that arise at merging or edge points in the limit of infinite matrix size. In particular and somewhat contrary to common expectations, the limiting statistics at merging points are not always governed by the Pearcey process. We will see a clear and comprehensive description of the cases in which the Pearcey process, the Airy line ensemble, or an interpolating process make their appearance at merging points. This is joint work with Thorsten Neuschel.