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Random Matrix Theory

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References and Further Reading

  • Bai ZD (1999) Methodologies in spectral analysis of large dimensional random matrices: a review. Stat Sinica 9(3):611–677

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  • Bai ZD (1993a) Convergence rate of expected spectral distributions of large random matrices. Part I. Wigner matrices. Ann Probab 21(2):625–648

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  • Bai ZD (1993b) Convergence rate of expected spectral distributions of large random matrices. Part II. Sample covariance matrices. Ann Probab 21(2):649–672

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  • Bai ZD, Silverstein JW (2004) CLT for linear spectral statistics of large-dimensional sample covariance matrices. Ann Probab 32(1):553–605

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  • Bai ZD, Silverstein JW (1999) Exact separation of eigenvalues of large dimensional sample covariance matrices. Ann Probab 27(3):1536–1555

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  • Bai ZD, Yao JF (2005) On the convergence of the spectral empirical process of Wigner matrices. Bernoulli 11(6):1059–1092

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  • Silverstein JW (1979) On the randomness of eigenvectors generated from networks with random topologies. SIAM J Appl Math 37:235–245

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  • Tracy CA, Widom H (1994) Level-spacing distributions and the Airy kernel. Commun Math Phys 159:151–174

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  • Wigner EP (1955) Characteristic vectors bordered matrices with infinite dimensions. Ann Math 62:548–564

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  • Wigner EP (1958) On the distributions of the roots of certain symmetric matrices. Ann Math 67:325–327

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  • Zheng S (2010) Central limit theorem for linear spectral statistics of large dimensional F-Matrix, to appear in Ann Inst Henri Poincaré Probab Stat

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Author information

Authors and Affiliations

  1. North Carolina State University, Raleigh, NC, USA

    Jack W. Silverstein (Professor)

Authors
  1. Jack W. Silverstein
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Editor information

Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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© 2011 Springer-Verlag Berlin Heidelberg

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Silverstein, J.W. (2011). Random Matrix Theory. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_472

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