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
This publication has 24 references indexed in Scilit:
- Lattice QCD spectra at finite temperature: a random matrix approachPhysics Letters B, 1996
- QCD-inspired spectra from Blue's functionsPhysics Letters B, 1996
- Random Matrix Model of QCD at Finite Density and the Nature of the Quenched LimitPhysical Review Letters, 1996
- Limit laws for Random matrices and free productsInventiones Mathematicae, 1991
- Learning in Neural Networks: Solvable DynamicsEurophysics Letters, 1989
- Spectrum of Large Random Asymmetric MatricesPhysical Review Letters, 1988
- Statistical theory of nuclear reactions and the Gaussian orthogonal ensembleAnnals of Physics, 1984
- On the spectrum of random matricesTheoretical and Mathematical Physics, 1972
- Statistical Ensembles of Complex, Quaternion, and Real MatricesJournal of Mathematical Physics, 1965
- Berechnung der natürlichen Linienbreite auf Grund der Diracschen LichttheorieThe European Physical Journal A, 1930