IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v35y2022i1d10.1007_s10959-020-01048-3.html
   My bibliography  Save this article

Random Perturbations of Matrix Polynomials

Author

Listed:
  • Patryk Pagacz

    (Jagiellonian University)

  • Michał Wojtylak

    (Jagiellonian University)

Abstract

A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of the resolvent of the sum is derived, and the eigenvalues are localised. Four instances are considered: a low-rank matrix perturbed by the Wigner matrix, a product HX of a fixed diagonal matrix H and the Wigner matrix X and two special matrix polynomials of higher degree. The results are illustrated with various examples and numerical simulations.

Suggested Citation

  • Patryk Pagacz & Michał Wojtylak, 2022. "Random Perturbations of Matrix Polynomials," Journal of Theoretical Probability, Springer, vol. 35(1), pages 52-88, March.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01048-3
    DOI: 10.1007/s10959-020-01048-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-020-01048-3
    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/s10959-020-01048-3?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.

    References listed on IDEAS

    as
    1. Jean Rochet, 2017. "Complex Outliers of Hermitian Random Matrices," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1624-1654, December.
    2. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Shocks in financial markets, price expectation, and damped harmonic oscillators," Papers 1103.1992, arXiv.org, revised Sep 2011.
    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.

      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:35:y:2022:i:1:d:10.1007_s10959-020-01048-3. 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.

      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.