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On the Limiting Distribution of the Spectra of Random Block Matrices

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  • Alexander N. Tikhomirov

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

Abstract

The behavior of the spectra of symmetric block-type random matrices with symmetric blocks of high dimensionality is considered in this paper. Under minimal conditions regarding the distributions of matrix block elements (Lindeberg conditions), the universality of the limiting empirical distribution function of block-type random matrices is shown.

Suggested Citation

  • Alexander N. Tikhomirov, 2025. "On the Limiting Distribution of the Spectra of Random Block Matrices," Mathematics, MDPI, vol. 13(13), pages 1-23, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2056-:d:1684015
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    References listed on IDEAS

    as
    1. Alexander Tikhomirov & Sabina Gulyaeva & Dmitry Timushev, 2024. "Limit Theorems for Spectra of Circulant Block Matrices with Large Random Blocks," Mathematics, MDPI, vol. 12(14), pages 1-16, July.
    2. Holger Dette & Bettina Reuther, 2010. "Random Block Matrices and Matrix Orthogonal Polynomials," Journal of Theoretical Probability, Springer, vol. 23(2), pages 378-400, June.
    3. Yi-Ting Li & Dang-Zheng Liu & Zheng-Dong Wang, 2011. "Limit Distributions of Eigenvalues for Random Block Toeplitz and Hankel Matrices," Journal of Theoretical Probability, Springer, vol. 24(4), pages 1063-1086, December.
    4. Dang-Zheng Liu & Zheng-Dong Wang, 2011. "Limit Distribution of Eigenvalues for Random Hankel and Toeplitz Band Matrices," Journal of Theoretical Probability, Springer, vol. 24(4), pages 988-1001, December.
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