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Spectral Measures of Spiked Random Matrices

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  • Nathan Noiry

    (UPL, Université Paris Nanterre)

Abstract

We study two spiked models of random matrices under general frameworks corresponding, respectively, to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the limiting spectral measure in the direction of an eigenvector of the perturbation leads to old and new results on the coordinates of eigenvectors.

Suggested Citation

  • Nathan Noiry, 2021. "Spectral Measures of Spiked Random Matrices," Journal of Theoretical Probability, Springer, vol. 34(2), pages 923-952, June.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-020-00987-1
    DOI: 10.1007/s10959-020-00987-1
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    References listed on IDEAS

    as
    1. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    2. Silverstein, J. W. & Choi, S. I., 1995. "Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 295-309, August.
    3. M. Capitaine, 2013. "Additive/Multiplicative Free Subordination Property and Limiting Eigenvectors of Spiked Additive Deformations of Wigner Matrices and Spiked Sample Covariance Matrices," Journal of Theoretical Probability, Springer, vol. 26(3), pages 595-648, September.
    Full references (including those not matched with items on IDEAS)

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