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Limit Theorems for Spectra of Circulant Block Matrices with Large Random Blocks

Author

Listed:
  • Alexander Tikhomirov

    (Institute of Physics and Mathematics, Komi SC UB RAS, Syktyvkar 167982, Russia)

  • Sabina Gulyaeva

    (Institute of Exact Sciences and IT, Pitirim Sorokin Syktyvkar State University, Syktyvkar 167001, Russia)

  • Dmitry Timushev

    (Institute of Physics and Mathematics, Komi SC UB RAS, Syktyvkar 167982, Russia)

Abstract

This paper investigates the spectral properties of block circulant matrices with high-order symmetric (or Hermitian) blocks. We analyze cases with dependent or sparse independent entries within these blocks. Additionally, we analyze the distribution of singular values for the product of independent circulant matrices with non-Hermitian blocks.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2291-:d:1440367
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    References listed on IDEAS

    as
    1. Murat Koloğlu & Gene S. Kopp & Steven J. Miller, 2013. "The Limiting Spectral Measure for Ensembles of Symmetric Block Circulant Matrices," Journal of Theoretical Probability, Springer, vol. 26(4), pages 1020-1060, December.
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