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The Subdominant Eigenvalue of a Large Stochastic Matrix

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  • Gyorgy Molnar
  • Andras Simonovits

Abstract

Using 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 Info

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

Volume (Year): 10 (1998)
Issue (Month): 1 ()
Pages: 79-82

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Handle: RePEc:taf:ecsysr:v:10:y:1998:i:1:p:79-82

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Related research

Keywords: Convergence; large systems; stochastic matrices;

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Cited by:
  1. Christian Bidard & Tom Schatteman, 2001. "The Spectrum of Random Matrices," Economic Systems Research, Taylor & Francis Journals, vol. 13(3), pages 289-298.
  2. 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.
  3. Andras Brody, 2000. "The Monetary Multiplier," Economic Systems Research, Taylor & Francis Journals, vol. 12(2), pages 215-219.

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