Tom Claeys
(Katholieke Universiteit Eindhoven)
Universality of the double scaling limit in critical random matrix ensembles
We study critical unitary random matrix ensembles where the limiting mean eigenvalue density vanishes quadratically at some interior point of the support. We establish universality of the eigenvalue correlation kernel near this critical point in a double scaling limit, thereby extending a result of Bleher and Its. This involves functions linked to the Hastings-McLeod solution of the Painlev\'e II equation. The main tools we use are equilibrium measures and Riemann-Hilbert problems.