IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v24y2011i4d10.1007_s10959-010-0326-3.html
   My bibliography  Save this article

Limit Distributions of Eigenvalues for Random Block Toeplitz and Hankel Matrices

Author

Listed:
  • Yi-Ting Li

    (Peking University)

  • Dang-Zheng Liu

    (Peking University)

  • Zheng-Dong Wang

    (Peking University)

Abstract

Block Toeplitz and Hankel matrices arise in many aspects of applications. In this paper, we will research the distributions of eigenvalues for some models and get the semicircle law. Firstly we will give trace formulas of block Toeplitz and Hankel matrix. Then we will prove that the almost sure limit $\gamma_{T}^{(m)}$ $(\gamma_{H}^{(m)})$ of eigenvalue distributions of random block Toeplitz (Hankel) matrices exist and give the moments of the limit distributions where m is the order of the blocks. Then we will prove the existence of almost sure limit of eigenvalue distributions of random block Toeplitz and Hankel band matrices and give the moments of the limit distributions. Finally we will prove that $\gamma_{T}^{(m)}$ $(\gamma_{H}^{(m)})$ converges weakly to the semicircle law as m→∞.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:24:y:2011:i:4:d:10.1007_s10959-010-0326-3
    DOI: 10.1007/s10959-010-0326-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-010-0326-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-010-0326-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Philippe Loubaton, 2016. "On the Almost Sure Location of the Singular Values of Certain Gaussian Block-Hankel Large Random Matrices," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1339-1443, December.
    2. Maurya, Shambhu Nath, 2024. "Limiting spectral distribution of Toeplitz and Hankel matrices with dependent entries," Statistics & Probability Letters, Elsevier, vol. 209(C).
    3. Debapratim Banerjee & Arup Bose, 2016. "Bulk behaviour of some patterned block matrices," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(2), pages 273-289, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jotpro:v:24:y:2011:i:4:d:10.1007_s10959-010-0326-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.