The Spectrum of Random Matrices
AbstractThe 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 InfoIf 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.
Bibliographic InfoArticle provided by Taylor and Francis Journals in its journal Economic Systems Research.
Volume (Year): 13 (2001)
Issue (Month): 3 ()
Contact details of provider:
Web page: http://taylorandfrancis.metapress.com/link.asp?target=journal&id=104572
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.:
- Gyorgy Molnar & Andras Simonovits, 1998. "The Subdominant Eigenvalue of a Large Stochastic Matrix," Economic Systems Research, Taylor and Francis Journals, vol. 10(1), pages 79-82.
- Stanisław Białas & Henryk Gurgul, 1998. "On Hypothesis about the Second Eigenvalue of the Leontief Matrix," Economic Systems Research, Taylor and Francis Journals, vol. 10(3), pages 285-290.
- 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.
- repec:mcd:mcddps:2012_06 is not listed on IDEAS
- Mariolis, Theodore & Tsoulfidis, Lefteris, 2012. "On Bródy’s conjecture: facts and figures from the US economy," MPRA Paper 43719, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty).
If references are entirely missing, you can add them using this form.