The Subdominant Eigenvalue of a Large Stochastic Matrix
AbstractUsing intuition and computer experimentation, Brady conjectured that the ratio of the subdominant eigenvalue to the dominant eigenvalue of a positive random matrix (with identically and independently distributed entries) converges to zero when the number of the sectors tends to infinity. In this paper, we discuss the deterministic case and, among other things, prove the following version of this conjecture: if each entry of the matrix deviates from 1/n by at most θ/n1+е, then the modulus of the subdominant root is at most θ/nе where θ and ε are arbitrary positive real parameters.
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Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Economic Systems Research.
Volume (Year): 10 (1998)
Issue (Month): 1 ()
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- Christian Bidard & Tom Schatteman, 2001. "The Spectrum of Random Matrices," Economic Systems Research, Taylor & Francis Journals, vol. 13(3), pages 289-298.
- Theodore Mariolis & Lefteris Tsoulfidis, 2012.
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Discussion Paper Series
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