We review some recent techniques for dealing with non-hermitian random matrix models based on generalized Green's functions. We introduce the diagrammatic methods in the hermitian case and generalize them to the non-hermitian case. The results are illustrated in terms of the eigenvalue distribution, eigenvector statistics and addition laws.
Janik, R. A., Nowak, M. A., Papp, G., & Zahed, I. (2001). Green’s functions in non-hermitian random matrix models. Physica E: Low-Dimensional Systems and Nanostructures, 9(3), 456–462. https://doi.org/10.1016/S1386-9477(00)00244-7