A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge for random symmetric matrices

Functional Analysis and its Applications

Volumn 32, Issue 2, 1998, Pages 114-131

  Sinai, Ya G ^a   Soshnikov, A B ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0343861172     PISSN: 00162663     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02482597     Document Type: Article

References (21)

1. E. Wigner, "Characteristic vectors of bordered matrices with infinite dimensions," Ann. Math., 62, 548-564 (1955).
2. E. Wigner, "On the distribution of the roots of certain symmetric matrices," Ann. Math. 67, 325-328 (1958).
3. V. A. Marchenko and L. A. Pastur, "The distribution of the eigenvalues in some ensembles of random matrices," Mat. Sb., 72, 507-536 (1967).
4. L. A. Pastur, "On the spectrum of random matrices," Teor. Mat. Fiz., 10, 102-112 (1972).
5. L. A. Pastur, "The spectra of random self-adjoint operators," Usp. Mat. Nauk, 28, 3-64 (1973).
6. L. Arnold, "On the asymptotic distribution of the eigenvalues of random matrices," J. Math. Anal. Appl., 20, 262-268 (1967).
7. L. Arnold, "On Wigner's semicircle law for the eigenvalues of random matrices," Z. Wahrscheinlichkeitstheorie Verw. Gebiete, 19, 191-198 (1971).
8. K. W. Wachter, "The strong limits of random matrix spectra for sample matrices of independent elements," Ann. Probab., 6, No. 1, 1-18 (1978).
9. V. L. Girko, The Spectral Theory of Random Matrices [in Russian], Nauka, Moscow, 1988.
10. Z. D. Bai, "Convergence rate of expected spectral distributions of large random matrices. I. Wigner Matrices," Ann. Probab., 21, 625-648 (1993).
11. A. M. Khorunzhy, B. A. Khoruzhenko, L. A. Pastur, and M. V. Shcherbina, "The large n-limit in statistical mechanics and the spectral theory of disordered systems," in: Phase Transitions and Critical Phenomena, Vol. 15 (C. Domb and J. L. Lebowitz, eds.), Academic Press, London, 1992.
12. A. M. Khorunzhy, B. A. Khoruzhenko, and L. A. Pastur, "Asymptotic properties of large random matrices with independent entries," J. Math. Phys., 37, 5033-5059 (1996).
13. A. Khorunzhy, "On smoothed density of states for Wigner random matrices," Random Oper. Stochastic Equations, 5, No. 2, 147-162 (1997).
14. Ya. Sinai and A. Soshnikov, "Central limit theorem for traces of large random symmetric matrices with independent matrix elements," Bol. Soc. Brasil. Mat., 29, No. 1, 1-24 (1998).
15. C. Tracy and H. Widom, "On orthogonal and symplectic matrix ensembles," Commun. Math. Phys., 177, 727-754 (1996).
16. C. Tracy and H. Widom, "Level-spacing distribution and the Airy kernel," Commun. Math. Phys., 159, 151-174 (1994).
17. P. J. Forrester, "The spectrum edge of random matrix ensembles," Nucl. Phys. B, 402, 709-728 (1994).
18. Z. Füredi and J. Komlóz, "The eigenvalues of random symmetric matrices," Combinatorica, 1, No. 3, 233-241 (1981).
19. A. Boutet de Monvel and M. V. Shcherbina, "On the norm of random matrices," Mat. Zametki, 57, No. 5, 688-698 (1995).
20. M. L. Mehta, Random Matrices, Academic Press, New York, 1991.
21. O. Costin and J. L. Lebowitz, "Gaussian fluctuations in random matrices," Phys. Rev. Lett., 75, No. 1, 69-72 (1995).