Skip to main content
Log in

Limit laws for Random matrices and free products

  • Published:
Inventiones mathematicae Aims and scope

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

References

  1. Arnold, L.: Deterministic version of Wigner's semicircle law for the distribution of matrix eigenvalues. Linear Algebra Appl.13, 185–199 (1976)

    Article  MATH  Google Scholar 

  2. Cuntz, J.: SimpleC *-algebras generated by isometries. Commun. Math. Phys.57, 173–185 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  3. Evans, D.E.: OnO n . Publ. Res. Inst. Math. Sci.16, 915–927 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gromov, M., Milman, V.D.: A topological application of the isoperimetric inequality. Am. J. Math.105, 843–854 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  5. Girko, V.L.: Random matrices. Kiev 1975 (In russian)

  6. Mehta, M.L.: Random matrices and the statistical theory of energy levels. New York: Academic Press, 1967

    MATH  Google Scholar 

  7. Paschke, W., Salinas, N.: Matrix algebras overO n Mich. Math. J.26, 3–12 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  8. Pimsner, M., Popa, S.: The ext-groups of someC *-algebras considered by J. Cuntz. Rev. Roum. Math. Pures Appl.23, 1069–1076 (1978)

    MathSciNet  MATH  Google Scholar 

  9. Silverstein, J.: Eigenvalues and eigenvectors of large dimensional sample covariance matrices (Random matrices and their applications). Contemp. Math.50, 153–160 (1986)

    Article  MathSciNet  Google Scholar 

  10. Szarek, S.J.: Spaces with large distance tol n and random matrices. Preprint IHES, 1988

  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 1985

    Chapter  Google Scholar 

  12. Voiculescu, D.: Addition of certain non-commuting random variables. J. Funct. Anal.66 (3), 323–346 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  13. Voiculescu, D.: Multiplication of certain non-commuting random variables. J. Oper. Theory18, 223–235 (1987)

    MathSciNet  MATH  Google Scholar 

  14. Voiculescu, D.: Operations on certain non-commutative operator-valued random variables (preliminary version). INCREST Preprint No. 42/1986

  15. Voiculescu, D.: Non-commutative random variables and spectral problems in free productC *-algebras. Preprint 1988 (to appear in Rocky Mt. J. Math.)

  16. Wachter, K.W.: The strong limits of random matrix spectra for sample matrices of independent elements. Ann. Probab.6, 1–18 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wigner, E.: Characteristic vectors of bordered matrices with infinite dimensions. Ann. Math.62, 548–564 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  18. Wigner, E.: On the distribution of the roots of certain symmetric matrices. Ann. Math.67, 325–327 (1958)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Oblatum 25-VI-1990

Research supported in part by a grant form the National Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voiculescu, D. Limit laws for Random matrices and free products. Invent. math. 104, 201–220 (1991). https://doi.org/10.1007/BF01245072

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01245072

Keywords

Navigation