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Inventiones mathematicae

, Volume 104, Issue 1, pp 201–220 | Cite as

Limit laws for Random matrices and free products

  • Dan Voiculescu
Article

Keywords

Random Matrice Limit Distribution Free Product Standard Family Free Convolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Arnold, L.: Deterministic version of Wigner's semicircle law for the distribution of matrix eigenvalues. Linear Algebra Appl.13, 185–199 (1976)CrossRefMATHGoogle Scholar
  2. 2.
    Cuntz, J.: SimpleC *-algebras generated by isometries. Commun. Math. Phys.57, 173–185 (1977)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Evans, D.E.: OnO n. Publ. Res. Inst. Math. Sci.16, 915–927 (1980)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Gromov, M., Milman, V.D.: A topological application of the isoperimetric inequality. Am. J. Math.105, 843–854 (1983)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Girko, V.L.: Random matrices. Kiev 1975 (In russian)Google Scholar
  6. 6.
    Mehta, M.L.: Random matrices and the statistical theory of energy levels. New York: Academic Press, 1967MATHGoogle Scholar
  7. 7.
    Paschke, W., Salinas, N.: Matrix algebras overO n Mich. Math. J.26, 3–12 (1979)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Pimsner, M., Popa, S.: The ext-groups of someC *-algebras considered by J. Cuntz. Rev. Roum. Math. Pures Appl.23, 1069–1076 (1978)MathSciNetMATHGoogle Scholar
  9. 9.
    Silverstein, J.: Eigenvalues and eigenvectors of large dimensional sample covariance matrices (Random matrices and their applications). Contemp. Math.50, 153–160 (1986)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Szarek, S.J.: Spaces with large distance tol n and random matrices. Preprint IHES, 1988Google Scholar
  11. 11.
    Voiculescu, D.: Symmetries of some reduced free productC *-algebra. In: Operator algebras and their connections with topology and ergodic theory. (Lect. Notes Math., vol. 1132, pp. 556–588) Berlin Heidelberg New York: Springer 1985CrossRefGoogle Scholar
  12. 12.
    Voiculescu, D.: Addition of certain non-commuting random variables. J. Funct. Anal.66 (3), 323–346 (1986)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Voiculescu, D.: Multiplication of certain non-commuting random variables. J. Oper. Theory18, 223–235 (1987)MathSciNetMATHGoogle Scholar
  14. 14.
    Voiculescu, D.: Operations on certain non-commutative operator-valued random variables (preliminary version). INCREST Preprint No. 42/1986Google Scholar
  15. 15.
    Voiculescu, D.: Non-commutative random variables and spectral problems in free productC *-algebras. Preprint 1988 (to appear in Rocky Mt. J. Math.)Google Scholar
  16. 16.
    Wachter, K.W.: The strong limits of random matrix spectra for sample matrices of independent elements. Ann. Probab.6, 1–18 (1978)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Wigner, E.: Characteristic vectors of bordered matrices with infinite dimensions. Ann. Math.62, 548–564 (1955)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Wigner, E.: On the distribution of the roots of certain symmetric matrices. Ann. Math.67, 325–327 (1958)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Dan Voiculescu
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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