Rank one non-Hermitian perturbations of Hermitian $β$-ensembles
Rostyslav Kozhan·2015-10-15·via math.PR updates on arXiv.org
For any $β>0$, we provide a tridiagonal matrix model and compute the joint eigenvalue density of a random rank one non-Hermitian perturbation of Gaussian and Laguerre $β$-ensembles of random matrices.