Bulk universality for complex eigenvalues of real non-symmetric random matrices

We will discuss non-Hermitian random matrix models, namely the universality problem for local eigenvalue statistics. The main result is universality in the bulk (i.e., away from the edge of the limiting spectrum) for complex eigenvalues of real non-symmetric matrices with i.i.d. entries. The method is based on exact computations (e.g., supersymmetric methods and duality formulas) combined with perturbation theory.

This is joint work with Sofiia Dubova.