Seminar

Abstract:
For general classes random Hermitian matrices, the eigenvalue statistics
at the edge of the spectrum are described by the Airy kernel; in
particular, the largest eigenvalue is asymptotically Tracy-Widom
distributed. This is in contrast with ensembles of complex random matrices
without symmetry conditions imposed, where extreme eigenvalues are
typically independent in the large n limit. We will discuss two families
of ensembles interpolating between these extremes, and show that the
spectral edge scaling limit in both cases is a family of two-dimensional
generalized Airy point processes