Non-Hermitian random matrix models: Free random variable approach

Romuald A. Janik, Maciej A. Nowak, Gábor Papp, Jochen Wambach, Ismail Zahed

Research output: Contribution to journalArticle

68 Citations (Scopus)

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 languageEnglish
Pages (from-to)4100-4106
Number of pages7
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume55
Issue number4
DOIs
Publication statusPublished - 1997

ASJC Scopus subject areas

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

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