### 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)].

Original language | English |
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Pages (from-to) | 4100-4106 |

Number of pages | 7 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 55 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1997 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*55*(4), 4100-4106. https://doi.org/10.1103/PhysRevE.55.4100