IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v16y2003i3d10.1023_a1025616431496.html
   My bibliography  Save this article

Permutation Matrices, Wreath Products, and the Distribution of Eigenvalues

Author

Listed:
  • Kelly Wieand

    (University of Chicago)

Abstract

We consider a class of random matrix ensembles which can be constructed from the random permutation matrices by replacing the nonzero entries of the n×n permutation matrix matrix with M×M diagonal matrices whose entries are random Kth roots of unity or random points on the unit circle. Let X be the number of eigenvalues lying in a specified arc I of the unit circle, and consider the standardized random variable (X−E[X])/(Var(X))1/2. We show that for a fixed set of arcs I 1,...,I N , the corresponding standardized random variables are jointly normal in the large n limit, and compare the covariance structures which arise with results for other random matrix ensembles.

Suggested Citation

  • Kelly Wieand, 2003. "Permutation Matrices, Wreath Products, and the Distribution of Eigenvalues," Journal of Theoretical Probability, Springer, vol. 16(3), pages 599-623, July.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:3:d:10.1023_a:1025616431496
    DOI: 10.1023/A:1025616431496
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1025616431496
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1025616431496?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. Hambly, B. M. & Keevash, P. & O'Connell, N. & Stark, D., 2000. "The characteristic polynomial of a random permutation matrix," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 335-346, December.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Valentin Bahier & Joseph Najnudel, 2022. "On Smooth Mesoscopic Linear Statistics of the Eigenvalues of Random Permutation Matrices," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1640-1661, September.
    2. Valentin Bahier, 2019. "On the Number of Eigenvalues of Modified Permutation Matrices in Mesoscopic Intervals," Journal of Theoretical Probability, Springer, vol. 32(2), pages 974-1022, June.

    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. Valentin Bahier, 2019. "On the Number of Eigenvalues of Modified Permutation Matrices in Mesoscopic Intervals," Journal of Theoretical Probability, Springer, vol. 32(2), pages 974-1022, June.
    2. Dang, K. & Zeindler, D., 2014. "The characteristic polynomial of a random permutation matrix at different points," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 411-439.
    3. Bahier, Valentin, 2019. "Characteristic polynomials of modified permutation matrices at microscopic scale," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4335-4365.
    4. Dirk Zeindler, 2013. "Central Limit Theorem for Multiplicative Class Functions on the Symmetric Group," Journal of Theoretical Probability, Springer, vol. 26(4), pages 968-996, December.
    5. Chafaï, Djalil, 2010. "The Dirichlet Markov Ensemble," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 555-567, March.

    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:16:y:2003:i:3:d:10.1023_a:1025616431496. 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: 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.