IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v209y2024ics0167715224000610.html
   My bibliography  Save this article

Limiting spectral distribution of Toeplitz and Hankel matrices with dependent entries

Author

Listed:
  • Maurya, Shambhu Nath

Abstract

This article deals with the limiting spectral distributions (LSD) of symmetric Toeplitz and Hankel matrices with dependent entries. For any fixed integer m≥0, we consider these n×n matrices with entries {Yj(m)/n;j∈Z}, where Yj(m)=∑r=−mmXj+r and {Xk} are i.i.d. random variables with mean zero and variance one. We provide explicit expressions for the LSDs. As a special case (m=0), this article provides an alternate proof for the LSDs of these matrices when the entries are i.i.d. with mean zero and variance one. The method is based on the moment method.

Suggested Citation

  • Maurya, Shambhu Nath, 2024. "Limiting spectral distribution of Toeplitz and Hankel matrices with dependent entries," Statistics & Probability Letters, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:stapro:v:209:y:2024:i:c:s0167715224000610
    DOI: 10.1016/j.spl.2024.110092
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224000610
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110092?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.

    References listed on IDEAS

    as
    1. Christopher Hammond & Steven J. Miller, 2005. "Distribution of Eigenvalues for the Ensemble of Real Symmetric Toeplitz Matrices," Journal of Theoretical Probability, Springer, vol. 18(3), pages 537-566, July.
    2. Bose, Arup & Mitra, Joydip, 2002. "Limiting spectral distribution of a special circulant," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 111-120, November.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arup Bose & Rajat Subhra Hazra & Koushik Saha, 2011. "Spectral Norm of Circulant-Type Matrices," Journal of Theoretical Probability, Springer, vol. 24(2), pages 479-516, June.
    2. 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.
    3. Steven Jackson & Steven J. Miller & Thuy Pham, 2012. "Distribution of Eigenvalues of Highly Palindromic Toeplitz Matrices," Journal of Theoretical Probability, Springer, vol. 25(2), pages 464-495, June.
    4. S. Chatterjee & A. Bose, 2004. "A New Method for Bounding Rates of Convergence of Empirical Spectral Distributions," Journal of Theoretical Probability, Springer, vol. 17(4), pages 1003-1019, October.
    5. Bose, Arup & Guha, Suman & Hazra, Rajat Subhra & Saha, Koushik, 2011. "Circulant type matrices with heavy tailed entries," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1706-1716, November.
    6. 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.
    7. Arup Bose & Joydip Mitra & Arnab Sen, 2012. "Limiting Spectral Distribution of Random k-Circulants," Journal of Theoretical Probability, Springer, vol. 25(3), pages 771-797, September.
    8. Adam Massey & Steven J. Miller & John Sinsheimer, 2007. "Distribution of Eigenvalues of Real Symmetric Palindromic Toeplitz Matrices and Circulant Matrices," Journal of Theoretical Probability, Springer, vol. 20(3), pages 637-662, September.
    9. 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.
    10. 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.

    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:eee:stapro:v:209:y:2024:i:c:s0167715224000610. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.