Non-Hermitian random matrix models: Free random variable approach
- 1 April 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 55 (4) , 4100-4106
- https://doi.org/10.1103/physreve.55.4100
Abstract
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. 6, 1440 (1965); V. L. Girko, Spectral Theory of Random Matrices (in Russian) (Nauka, Moscow, 1988)] and Mahaux-Weidenmüller (chaotic resonance scattering) [C. Mahaux and H. A. Weidenmüller, Shell-model Approach to Nuclear Reactions (North-Holland, Amsterdam, 1969)].Keywords
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