Green's Functions in Non-hermitian Random Matrix Models

Abstract

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.

Based on talks by R.A. Janik at the CIRM workshop `Free probability and applications' Marseille 1998, and by M.A. Nowak at the MPI workshop on `Dynamics of Complex Systems' Dresden 1999. 8 pages, 3 figures, uses espcrc2.sty