Eigenvalue distribution of random operators and matrices

Leonid Pastur

Séminaire Bourbaki (1991-1992)

  • Volume: 34, page 445-461
  • ISSN: 0303-1179

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Pastur, Leonid. "Eigenvalue distribution of random operators and matrices." Séminaire Bourbaki 34 (1991-1992): 445-461. <http://eudml.org/doc/110162>.

@article{Pastur1991-1992,
author = {Pastur, Leonid},
journal = {Séminaire Bourbaki},
keywords = {random operators; integrated density of states; random matrices},
language = {eng},
pages = {445-461},
publisher = {Société Mathématique de France},
title = {Eigenvalue distribution of random operators and matrices},
url = {http://eudml.org/doc/110162},
volume = {34},
year = {1991-1992},
}

TY - JOUR
AU - Pastur, Leonid
TI - Eigenvalue distribution of random operators and matrices
JO - Séminaire Bourbaki
PY - 1991-1992
PB - Société Mathématique de France
VL - 34
SP - 445
EP - 461
LA - eng
KW - random operators; integrated density of states; random matrices
UR - http://eudml.org/doc/110162
ER -

References

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  1. [1] U. Grenander, G. Szegö, Toeplitz form and their applications, Univ. Calif. Press, Berkeley, 1958. Zbl0080.09501MR94840
  2. [2] R. Carmona, J. Lacroix, Spectral theory of the random Schrödinger operator, Birkhäuser, Basel, 1990. Zbl0717.60074MR1102675
  3. [3] L.A. Pastur, A.L. Figotin, Spectra of Random and Almost Periodic Operators, Grundlehren der Math. Wiss., Springer, Heidelberg, 1992. Zbl0752.47002MR1223779
  4. [4] M.L. Mehta, Random matrices, Academic Press, N. Y., 1967. Zbl0780.60014MR1083764
  5. [5] V. Girko, Spectral theory of random matrices, Nauka, Moscow, 1988. Zbl0656.15012MR955497
  6. [6] L.A. Pastur, Spectra of Random Self-Adjoint Operators, Russ. Math. Surveys, 28, 1 (1973), 1-67. Zbl0277.60049MR406251
  7. [7] D. Bessis, C. Itzykson, J. Zuber, Quantum field theory techniques, Adv. App. Math., 1, 2 (1980), 109-157. Zbl0453.05035MR603127
  8. [8] M. Kus, M. Lewenstein, F. Haake, Density of eigenvalues pf random band matrices, Phys. Review, A44 (1991), 2800-2808. MR1126835
  9. [9] L. Bogachev, S. Molchanov, L. Pastur, Teor. Matem. Fyz., 90 (1991), 31-42 (in Russian). MR1150631
  10. [10] A. Khorunzhy, S. Molchanov, L. Pastur, Teor. Matem. Fyz., 92, 2, (1992) (in Russian). 
  11. [11] A. Khorunzhy, B. Khoruzhenko, L. Pastur, M. Shcherbina, The Large-n Limit in Statistical Mechanics and Spectral Theory of Disordered Systems. In "Phase Transitions and Critical Phenomena", eds. C.Domb and J.L.Lebowitz, 15, 73, Academic Press, London, 1992. 
  12. [12] E. Brezin, V. Kazakov, Exactly solvable field theories of closed strings, Phys. Lett., B236, 2 (1990),144-150; M. Douglas, S. Shenker, Nucl. Phys., B335 (1990), 635; D. Gross, A. Migdal, Nonperturbative solution of the Ising model on a random surface, Phys. Rev. Lett., 64, 7 (1990), 717-720. MR1040213
  13. [13] D.S. Lubinsky, Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights, Pitman Research Notes in Math., 202, Longmans, Harlow, 1989. Zbl0743.41001MR999924
  14. [14] L. Pastur (in press). 
  15. [15] L. Pastur, V. Tkachenko (in preparation). 
  16. [16] A. Khorunzhy, L. Pastur (in preparation). 
  17. [17] F. Wegner, Disordered system with n orbitals per site: n = ∞ limit, Phys. Rev., B19 (1979), 783-792. 

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