Extreme eigenvalues and the emerging outlier in rank-one non-Hermitian deformations of the Gaussian Unitary Ensemble

Yan V. Fyodorov, Boris A. Khoruzhenko, Mihail Poplavskyi

Complex eigenvalues of random matrices $J=\text{GUE }+ iγ\diag (1, 0, \ldots, 0)$ provide the simplest model for studying resonances in wave scattering from a quantum chaotic syste…