Universality of the double scaling limit in unitary random matrix ensembles

Arno Kuijlaars


We consider unitary random matrix ensembles in the critical case where the limiting mean eigenvalue density vanishes quadratically at an interior point of the support. For the case of a quartic potential Bleher and Its obtained the double scaling limits of the eigenvalue correlation kernels at such a critical point. The limiting kernels are constructed out of functions associated with the second Painleve equation. We extend this result to general potentials.

(Based on joint work with Tom Claeys.)