Non-Hermitian random matrices beyond the circular law
It is a classical result of random matrix theory that under certain assumptions
the empirical eigenvalue distribution of Hermitian polynomials of random
matrices with i.i.d. entries converges to a limit described by free probability.
In many cases this convergence even holds down to local scales, i.e. the
spectral measure converges to an empirical density on all scales above the
typical eigenvalue spacing as the dimension of the matrix grows to infinity.
While no results on a similar level of generality exist for non-Hermitian
polynomials, progress has been made in recent years. In this talk I will discuss
techniques to prove local laws beyond the i.i.d. case and will present a novel
result for a specific ensemble of non-Hermitian random matrices.
Raum – 04.363