IDEAS home Printed from https://ideas.repec.org/a/taf/ecsysr/v20y2008i4p429-432.html
   My bibliography  Save this article

The First Two Eigenvalues of Large Random Matrices and Brody's Hypothesis on the Stability of Large Input-Output Systems

Author

Listed:
  • Guang-Zhen Sun

Abstract

Brody (1997) notices that for large random Leontief matrices, namely non-negative square matrices with all entries i.i.d., the ratio between the subdominant eigenvalue (in modulus) and the dominant eigenvalue declines generically to zero at a speed of the square root of the size of the matrix as the matrix size goes to infinity. Since then, several studies have been published in this journal in attempting to rigorously verify Brody's conjecture. This short article, drawing upon some theorems obtained in recent years in the literature on empirical spectral distribution of random matrices, offers a short proof of Brody's conjecture, and discusses briefly some related issues.

Suggested Citation

  • Guang-Zhen Sun, 2008. "The First Two Eigenvalues of Large Random Matrices and Brody's Hypothesis on the Stability of Large Input-Output Systems," Economic Systems Research, Taylor & Francis Journals, vol. 20(4), pages 429-432.
  • Handle: RePEc:taf:ecsysr:v:20:y:2008:i:4:p:429-432
    DOI: 10.1080/09535310802551471
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/09535310802551471
    Download Restriction: Access to full text is restricted to subscribers.

    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. Theodore Mariolis & Lefteris Tsoulfidis, 2012. "On Brody’S Conjecture: Facts And Figures From The Us Economy," Discussion Paper Series 2012_06, Department of Economics, University of Macedonia, revised May 2012.

    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:taf:ecsysr:v:20:y:2008:i:4:p:429-432. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: http://www.tandfonline.com/CESR20 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.