Advanced Search
MyIDEAS: Login to save this article or follow this journal

The Spectrum of Random Matrices


Author Info

  • Christian Bidard
  • Tom Schatteman


The Frobenius eigenvector of a positive square matrix is obtained by iterating the multiplication of an arbitrary positive vector by the matrix. Brody (1997) noticed that, when the entries of the matrix are independently and identically distributed, the speed of convergence increases statistically with the dimension of the matrix. As the speed depends on the ratio between the subdominant and the dominant eigenvalues, Brody's conjecture amounts to stating that this ratio tends to zero when the dimension tends to infinity. The paper provides a simple proof of the result. Some mathematical and economic aspects of the problem are discussed.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL:
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Economic Systems Research.

Volume (Year): 13 (2001)
Issue (Month): 3 ()
Pages: 289-298

as in new window
Handle: RePEc:taf:ecsysr:v:13:y:2001:i:3:p:289-298

Contact details of provider:
Web page:

Order Information:

Related research

Keywords: Brodyy; Dominant Eigenvalues; Frobenius;


References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Dietzenbacher, Erik, 1993. "A limiting property for the powers of a non-negative, reducible matrix," Structural Change and Economic Dynamics, Elsevier, vol. 4(2), pages 353-366, December.
  2. Stanisław Białas & Henryk Gurgul, 1998. "On Hypothesis about the Second Eigenvalue of the Leontief Matrix," Economic Systems Research, Taylor & Francis Journals, vol. 10(3), pages 285-290.
  3. Gyorgy Molnar & Andras Simonovits, 1998. "The Subdominant Eigenvalue of a Large Stochastic Matrix," Economic Systems Research, Taylor & Francis Journals, vol. 10(1), pages 79-82.
Full references (including those not matched with items on IDEAS)


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

Cited by:
  1. Mariolis, Theodore & Tsoulfidis, Lefteris, 2012. "On Bródy’s conjecture: facts and figures from the US economy," MPRA Paper 43719, University Library of Munich, Germany.


This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


Access and download statistics


When requesting a correction, please mention this item's handle: RePEc:taf:ecsysr:v:13:y:2001:i:3:p:289-298. 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: (Michael McNulty).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.