Almost Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre Eigenvalue Statistics
Abstract
By using the method of orthogonal polynomials, we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from Hermitian matrices characterized by the Wigner-Dyson statistics of real eigenvalues to strongly non-Hermitian ones whose complex eigenvalues were studied by Ginibre. Two-point statistical measures [as, e.g., spectral form factor, number variance, and small distance behavior of the nearest neighbor distance distribution p\(s\)] are studied in more detail. In particular, we found that the latter function may exhibit unusual behavior p\(s\)~s5/2 for some parameter values.
- Publication:
-
Physical Review Letters
- Pub Date:
- July 1997
- DOI:
- 10.1103/PhysRevLett.79.557
- arXiv:
- arXiv:cond-mat/9703152
- Bibcode:
- 1997PhRvL..79..557F
- Keywords:
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- Condensed Matter;
- High Energy Physics - Theory;
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 4 pages, RevTEX