The First Two Eigenvalues of Large Random Matrices and Brody's Hypothesis on the Stability of Large Input-Output Systems
AbstractBrody (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.
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 & Francis Journals in its journal Economic Systems Research.
Volume (Year): 20 (2008)
Issue (Month): 4 ()
Contact details of provider:
Web page: http://www.tandfonline.com/CESR20
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- 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.
- 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.