LETTER TO THE EDITOR: On universality of the smoothed eigenvalue density of large random matrices

We describe the resolvent approach for the rigorous study of the mesoscopic regime of Hermitian matrix spectra. We present results reflecting universal behaviour of the smoothed density of the eigenvalue distribution of large random matrices.

[1]  F. Dyson Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .

[2]  V. Marčenko,et al.  DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES , 1967 .

[3]  F. Dyson A Class of Matrix Ensembles , 1972 .

[4]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[5]  J. Jurkiewicz,et al.  Multiloop correlators for two-dimensional quantum gravity , 1990 .

[6]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[7]  B. M. Fulk MATH , 1992 .

[8]  A. Zee,et al.  Universality of the correlations between eigenvalues of large random matrices , 1993 .

[9]  L. Pastur,et al.  Limits of infinite interaction radius, dimensionality and the number of components for random operators with off-diagonal randomness , 1993 .

[10]  A. M. K. A. L. A. Pastur On the Eigenvalue distribution of the deformed Wigner ensemble of random matrices , 1994 .

[11]  Spectral operator theory and related topics , 1994 .

[12]  Boris A. Khoruzhenko,et al.  Asymptotic properties of large random matrices with independent entries , 1996 .

[13]  L. Pastur,et al.  Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles , 1997 .

[14]  T. Guhr,et al.  RANDOM-MATRIX THEORIES IN QUANTUM PHYSICS : COMMON CONCEPTS , 1997, cond-mat/9707301.

[15]  G. J. Rodgers,et al.  On the Wigner law in dilute random matrices , 1998 .

[16]  A. Boutet de Monvel,et al.  Asymptotic distribution of smoothed eigenvalue density. I. Gaussian random matrices , 1999 .

[17]  M. Stephanov,et al.  Random Matrices , 2005, hep-ph/0509286.