Matrices aléatoires : statistique asymptotique des valeurs propres

Leonid Pastur; Antoine Lejay

Séminaire de probabilités de Strasbourg (2002)

  • Volume: 36, page 135-164

How to cite

top

Pastur, Leonid, and Lejay, Antoine. "Matrices aléatoires : statistique asymptotique des valeurs propres." Séminaire de probabilités de Strasbourg 36 (2002): 135-164. <http://eudml.org/doc/114083>.

@article{Pastur2002,
author = {Pastur, Leonid, Lejay, Antoine},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {matrices aléatoires; ensemble gaussien orthogonal; ensemble gaussien unitaire; comportement asymptotique du spectre; loi du demi-cercle},
language = {fre},
pages = {135-164},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Matrices aléatoires : statistique asymptotique des valeurs propres},
url = {http://eudml.org/doc/114083},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Pastur, Leonid
AU - Lejay, Antoine
TI - Matrices aléatoires : statistique asymptotique des valeurs propres
JO - Séminaire de probabilités de Strasbourg
PY - 2002
PB - Springer - Lecture Notes in Mathematics
VL - 36
SP - 135
EP - 164
LA - fre
KW - matrices aléatoires; ensemble gaussien orthogonal; ensemble gaussien unitaire; comportement asymptotique du spectre; loi du demi-cercle
UR - http://eudml.org/doc/114083
ER -

References

top
  1. [AG] N.I. Akhiezer et I.M. Glazman. Theory of Linear Operators in Hilbrt Space, vol. 1. Dover, 1993. Zbl0874.47001MR1255973
  2. [AS] M. Abramowitz et I. Stegun. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. National Bureau of Standards,1964. Zbl0171.38503MR167642
  3. [CH] R. Courant et D. Hilbert. Methods of Mathematical Physics, vol. 1. Interscience, 1953. Zbl0051.28802MR65391
  4. [DK+] P. Deift, T. Kriecherbauer, K.T.-R. McLaughlin, S. Venakides et X. Zhou. Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure Appl. Math., vol. 52, pp. 1335-1425,1999. Zbl0944.42013MR1702716
  5. [Fo] P.J. Forrester. The spectrum edges of random matrices. Nuclear Phys., vol. B402, pp. 709-723, 1993. Zbl1043.82538MR1236195
  6. [Gi] V. Girko. Random Determinants. Kluwer, 1991. 
  7. [GMW] T. Guhr, A. Müller-Groeling et H.A. Weidenmüller. Random matrix theories in quantum physics: common concepts. Physics Report, vol. 299, pp. 189-425, 1998. MR1628467
  8. [He] P. Henrici. Applied and Computational Complex Analysis, vol. 2. Wiley, 1977. Zbl0363.30001MR453984
  9. [Jo] K. Johansson. On fluctuations of eigenvalues of random Hermitian matrices. Duke Math. J., vol. 91, pp. 151-204, 1998. Zbl1039.82504MR1487983
  10. [KS] N. Katz et P. Sarnak. Random Matrices, Frobenius Eigenvalues, and Monodromy. AMS, 1999 ; Zeros of zeta fonctions and symmetry. Bull. Amer. Math. Soc., vol. 36, pp. 1-26, 1999. Zbl0921.11047MR1640151
  11. [KKP] A. Khorunzhy, B. Khoruzhenko et L. Pastur. Random matrices with independant entries: asymptotic property of the Green function. J. Stat. Phys., vol. 37, pp. 5033-5066, 1996. Zbl0866.15014MR1411619
  12. [MP] V.A. Marchenko et L.A. Pastur. The eigenvalue distribution in some ensembles of random matrices. Math. USSR Sbornik vol. 1, pp. 457-483, 1996. Zbl0162.22501
  13. [Me] M.L. Mehta. Random Matrices. Academic Press, 1991. Zbl0780.60014MR1083764
  14. [Mi] N. Minami. Local fluctuation of the spectrum of a multidimensional Anderson tight binding model. Comm. Math. Phys., vol. 177, pp. 709-725, 1996. Zbl0851.60100MR1385082
  15. [Mu] R. Muirhead. Aspects of Multivariate Analysis. Wiley, 1982. MR652932
  16. [P1] L.A. Pastur. On the spectrum of random matrices. Teor. Math. Phys., vol. 10, pp. 67-74, 1972. MR475502
  17. [P2] L. Pastur. Spectral and probabilistic aspects of matrix models. Dans Algebraic and Geometric Methods in Mathematical Physics, pp. 207-242. Kluwer, 1996. Zbl0844.15009MR1385683
  18. [P3] L. Pastur. On a simple approach to global regime of random matrix theory. Dans Mathematical Results in Statistical Mechanics, pp. 429-454. World Scientific, Singapore, 1999. Zbl0996.15014MR1886270
  19. [P4] L. Pastur. Random matrices as paradigm. Dans Mathematical Physics 2000, pp. 216-265. Imperial College Press, Londres, 2000. Zbl1017.82023MR1773047
  20. [PS] L. Pastur et M. Shcherbina. Universality of the local eigenvalue statistics for a class of unitary, invariant ensembles. J. Stat. Phys., vol. 86, pp. 109-125, 1997. Zbl0916.15009MR1435193
  21. [PV] L. Pastur et V. VASIL'CHUK. On the law of addition of random matrices. Comm. Math. Phys., vol. 214, pp. 249-286, 2000. Zbl1039.82020MR1796022
  22. [Sp] R. Speicher. Free convolution and the random sum of matrices. Publ. Res. Inst. Math. Sci., vol. 5, pp. 731-744, 1993. Zbl0795.46048MR1245015
  23. [Sz] G. Szegö. Orthogonal Polynomials, volume XXIII de Colloquium Publications. American Mathematical Society, 1975. Zbl0305.42011MR372517
  24. [TW] C.A. Tracy et H. Widom. Introduction to Random Matrices. Dans Geometric and Quantum Aspects of Integrable Systems (Scheveningen, 1992), pp. 103-130. Springer, 1993. Zbl0791.15017MR1253763
  25. [VDN] D.-V. Voiculescu, K.J. Dykema et A. Nica. Free Random Variables. American Mathematical Society, 1992. Zbl0795.46049MR1217253
  26. [Vo] D.-V. Voiculescu (editor). Free Probability Theory. American Mathematical Society, 1997. Zbl0859.00025MR1426832

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.