Planar symplectic ensembles: from scaling limits to Wronskian structures
A talk in the Seminar Zufallsmatrizen series by
Sungsoo Byun
| Abstract: | In this talk, I will discuss complex eigenvalues of non-Hermitian random matrices with simplectic symmetry, which are known to form Pfaffian point processes. In particular, I will present various scaling limits of symplectic ensembles and explain their unified integrable structure of Wronskian form. Examples include edge scaling limits of the Ginibre ensemble (with boundary confinements) and bulk/edge scaling limits of the elliptic Ginibre ensemble in the almost-Hermitian regime. Beyond standard universality classes, I will also introduce scaling limits of Mittag-Leffler ensemble at the singularity. Furthermore, for symplectic ensembles with general external potentials, I will present the characterization of translation invariant scaling limits by virtue of rescaled mass-one and Ward's equations. This talk is based on two joint works: one with Gernot Akemann and Nam-Gyu Kang and the other Markus Ebke and Seong-Mi Seo. Please contact Gernot Akemann (akemann@physik.uni-bielefeld.de) for details regarding access. Within the CRC this talk is associated to the project(s): C6 |