Skip to main content
Log in

On the level density of random band matrices

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. E. P. Wigner, “On the distribution of the roots of certain symmetric matrices,” Ann. Math., 67, No. 2, 325–327 (1958).

    Google Scholar 

  2. E. P. Wigner, “Random matrices in physics,” SIAM Rev., 9, No. 1, 1–23 (1967).

    Google Scholar 

  3. M. L. Mehta, Random Matrices and the Statistical Theory of Energy Levels, Ann. Probab., Academic Press, New York (1967).

    Google Scholar 

  4. U. Grenander, Probabilities on Algebraic Structures, Wiley, New York (1963).

    Google Scholar 

  5. V. A. Marchenko and L. A. Pastur, “Distribution of eigenvalues in certain sets of random matrices,” Mat. Sb., 72 (114), No. 4, 507–536 (1967).

    Google Scholar 

  6. L. A. Pastur, “On the spectrum of random matrices,” Teor. Mat. Fiz., 10, No. 1, 102–112 (1972).

    Google Scholar 

  7. L. A. Pastur, “The spectra of random selfadjoint operators,” Usp. Mat. Nauk, 28, No. 1, 3–64 (1973).

    Google Scholar 

  8. V. L. Girko, Spectral Theory of Random Matrices [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  9. F. J. Dyson, “The dynamics of a disordered linear chain,” Physical Rev. (2), 92, No. 6, 1331–1338 (1953).

    Google Scholar 

  10. L. A. Pastur, “Spectral theory of random selfadjoint operators,” in: Itogi Nauki i Tekhniki, Ser. Teor. Veroyatn. Mat. Statist. Teor. Kibernet., VINITI, Moscow,25, (1987), pp. 3–67.

    Google Scholar 

  11. G. Casati, F. Izrailev, and L. Molinari, “Scaling properties of band random matrices,” Phys. Rev. Lett.,64, No. 16, 1851–1854 (1990).

    Google Scholar 

  12. F. M. Izrailev, “Simple models of quantum chaos: spectrum and eigenfunctions,” Phys. Rep., 196, No. 5–6, 299–392 (1990).

    Google Scholar 

  13. L. V. Bogachev, S. A. Molchanov, and L. A. Pastur, On the level densities of random symmetric band matrices. Preprint No. 119, Institute for Mathematics, Ruhr University, Bochum (1991).

    Google Scholar 

  14. W. Ledermann, “Asymptotic formulae relating to the physical theory of crystals,” Proc. Roy. Soc. London Ser. A, 182, 362–377 (1944).

    Google Scholar 

  15. K. W. Wachter, “The strong limits of random matrix spectra for sample matrices of independent elements,” Ann. Probab., 6, No. 1, 1–18 (1978).

    Google Scholar 

  16. Z. D. Bai and Y. Q. Yin, “Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix,” Ann. Probab., 16, No. 4, 1729–1741 (1988).

    Google Scholar 

  17. R. Bellman, Introduction to Matrix Analysis, McGraw-Hill, New York (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 50, No. 6, pp. 31–42, December, 1991.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bogachev, L.V., Molchanov, S.A. & Pastur, L.A. On the level density of random band matrices. Mathematical Notes of the Academy of Sciences of the USSR 50, 1232–1242 (1991). https://doi.org/10.1007/BF01158263

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158263

Keywords

Navigation