Edge universality for non-Hermitian random matrices

Summary

We prove that on the unit circle (the asymptotic boundary of the spectrum) the local eigenvalue statistics on non-Hermitian random matrices with IID entries are universal. This generalizes previous results on random matrices matching four Gaussian moments.

Abstract

We consider large non-Hermitian real or complex random matrices $X$ with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of $X$ are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.

Paper

1908.00969.pdf