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Zbl 0853.15021
Pastur, L.
Eigenvalue distribution of random matrices: Some recent results. (English)
[J] Ann. Inst. Henri Poincaré, Phys. Théor. 64, No.3, 325-337 (1996). ISSN 0246-0211

This expository article contains results on the eigenvalue distribution of $N \times N$ random symmetric (or Hermitian) matrices in asymptotics of $N \to \infty$. The main attention is paid to two random matrix ensembles consisting of random matrices with independent arbitrary distributed entries and random matrices with Gaussian weakly correlated entries.\par The limit $N \to \infty$ of the normalized eigenvalue counting function (NCF) and $1/N$-corrections to NCF are considered. Results concerning a smoothed eigenvalue density correlator are presented and the universality conjecture for local spectral properties of large random matrices is discussed.\par The random matrix ensemble consisting of random matrices with orthogonal (or unitary) invariant probability distribution is complementary to the random matrix ensembles mentioned above. The limiting NCF of this third ensemble was studied by {\it A. Boutet de Monvel}, {\it L. Pastur} and {\it M. Shcherbina} [Journ. Stat. Phys. 79, 585-613 (1995)].
[A.Khorunzhy (Khar'kov)]

MSC 2000:: *15A52 Random matrices
15A18 Eigenvalues of matrices, etc.

Keywords: eigenvalue distribution; random matrices; normalized eigenvalue counting function

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