New Developments In Non-Hermitian Random Matrix Models

In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a $1/N$ expansion (b) - A generalization of the addition theorem (R-transformation) (c) - A conformal transformation on the position of pertinent singularities (d) - A `phase' analysis using appropriate partition functions (e) - A number of two-point functions and the issue of universality.