Maurice Duits: Height fluctuations for non-intersecting path ensembles

Abstract: In this talk I will report on recent work on height fluctuations for ensembles of non-intersecting paths. In such ensembles one considers a finite number of random paths that connect giving starting and endpoints and that are conditioned   not to intersect.  Due to this non-intersecting condition we observe universal random matrix laws in the limit as the number of paths grows large. This talk focuses on a  new approach for studying the  fluctuations of the associated height function, where one expects the Gaussian Free Field to appear as  the universal law. To illustrate the results I will discuss the fluctuations of the  'watermelon' obtained by Dyson's Brownian Motion.