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Local Laws for Sparse Sample Covariance Matrices

Author

Listed:
  • Alexander N. Tikhomirov

    (Institute of Physics and Mathematics, Komi Science Center of Ural Branch of RAS, 167982 Syktyvkar, Russia)

  • Dmitry A. Timushev

    (Institute of Physics and Mathematics, Komi Science Center of Ural Branch of RAS, 167982 Syktyvkar, Russia)

Abstract

We proved the local Marchenko–Pastur law for sparse sample covariance matrices that corresponded to rectangular observation matrices of order n × m with n / m → y (where y > 0 ) and sparse probability n p n > log β n (where β > 0 ). The bounds of the distance between the empirical spectral distribution function of the sparse sample covariance matrices and the Marchenko–Pastur law distribution function that was obtained in the complex domain z ∈ D with Im z > v 0 > 0 (where v 0 ) were of order log 4 n / n and the domain bounds did not depend on p n while n p n > log β n .

Suggested Citation

  • Alexander N. Tikhomirov & Dmitry A. Timushev, 2022. "Local Laws for Sparse Sample Covariance Matrices," Mathematics, MDPI, vol. 10(13), pages 1-38, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2326-:d:854796
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    Cited by:

    1. Alexander N. Tikhomirov & Vladimir V. Ulyanov, 2023. "On the Special Issue “Limit Theorems of Probability Theory”," Mathematics, MDPI, vol. 11(17), pages 1-4, August.

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