Non-Hermitian random matrix models: Free random variable approach

Using the standard concepts of free random variables, we show that for a large class of non-Hermitian random matrix models, the support of the eigenvalue distribution follows from their Hermitian analogs using a conformal transformation. We also extend the concepts of free random variables to the class of non-Hermitian matrices, and apply them to the models discussed by Ginibre-Girko (elliptic ensemble) [J. Ginibre, J. Math. Phys. {bold 6}, 1440 (1965); V. L. Girko, {ital Spectral Theory of Random Matrices} (in Russian) (Nauka, Moscow, 1988)] and Mahaux-Weidenm{umlt u}ller (chaotic resonance scattering) [C. Mahaux and H. A. Weidenm{umlt u}ller, {ital Shell-model Approach to Nuclear Reactions} (North-Holland, Amsterdam, 1969)]. {copyright} {ital 1997} {ital The American Physical Society}