Non-Hermitian random matrix models: Free random variable approach
Journal Article
·
· Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
- GSI, Plankstrasse 1, D-64291 Darmstadt (Germany)
- Institute for Theoretical Physics, Eoetvoes University, Budapest (Hungary)
- Institut fuer Kernphysik, TH Darmstadt (Germany)
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}
- OSTI ID:
- 656916
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 4 Vol. 55; ISSN 1063-651X; ISSN PLEEE8
- Country of Publication:
- United States
- Language:
- English
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