Conformal Universality in Normal Matrix Ensembles

A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted increasing attention, however, questions on universality for these ensembles still remain under debate. We analyze the universality properties of random normal ensembles. We show that the concept of universality used for Hermitian ensembles cannot be directly extrapolated to normal ensembles. Moreover, we show that the eigenvalue statistics of random normal matrices with radially symmetric potential can be made universal under a conformal transformation.