Vincent Painchaud (McGill University)

Title: Operator level edge to bulk transitions in beta-ensembles via canonical systems.

Abstract: The stochastic Airy, Bessel and sine operators characterize the soft edge, hard edge and bulk scaling limits of beta-ensembles. The stochastic Airy and Bessel operators are both random Sturm-Liouville operators, but the stochastic sine operator is rather a random Dirac operator, which is a two-dimensional first-order differential operator. While these two classes of operators are distinct, they can both be represented as canonical systems, which gives a unified framework for defining their spectral data. In this talk, we will see how canonical systems theory can be used to prove that in suitable high-energy scaling limits, the stochastic Airy and Bessel operators converge to the stochastic sine operator. This is based on joint work with Elliot Paquette.

Zoom link: https://umontreal.zoom.us/j/83832644262?pwd=gQDOX4997Yehibng7GjtEKwUhqAqNV.1