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Distribution of Subdominant Eigenvalues of Random Matrices

Author

Listed:
  • G. Goldberg

    (Programming Recourses Company)

  • P. Okunev

    (University of Connecticut)

  • M. Neumann

    (University of Connecticut)

  • H. Schneider

    (University of Wisconsin)

Abstract

We mainly investigate the behavior of the subdominant eigenvalue of matrices B= (b i,j)∈ℝn,n whose entries are independent random variables with an expectation Eb i,j=1/n and with a variance n ≤ c/n 2 for some constant c ≥ 0. For such matrices we show that for large n, the subdominant eigenvalue is, with great probability, in a small neighborhood of 0. We also show that for large n, the spectral radius of such matrices is, with great probability, in a small neighborhood of 1.

Suggested Citation

  • G. Goldberg & P. Okunev & M. Neumann & H. Schneider, 2000. "Distribution of Subdominant Eigenvalues of Random Matrices," Methodology and Computing in Applied Probability, Springer, vol. 2(2), pages 137-151, August.
    • Handle: RePEc:spr:metcap:v:2:y:2000:i:2:d:10.1023_a:1010093922183
    DOI: 10.1023/A:1010093922183
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    Citations

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    Cited by:

    1. 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.
    2. Schefold, Bertram, 2023. "The rarity of reswitching explained," Structural Change and Economic Dynamics, Elsevier, vol. 67(C), pages 128-150.
    3. Anwar Shaikh & Luiza Nassif, 2018. "Eigenvalue distribution, matrix size and the linearity of wage-profit curves," Working Papers 1812, New School for Social Research, Department of Economics.
    4. Torres-González, Luis Daniel, 2022. "The Characteristics of the Productive Structure Behind the Empirical Regularities in Production Prices Curves," Structural Change and Economic Dynamics, Elsevier, vol. 62(C), pages 622-659.
    5. Iliadi, Fotoula & Mariolis, Theodore & Soklis, George & Tsoulfidis, Lefteris, 2012. "Bienenfeld’s approximation of production prices and eigenvalue distribution: some more evidence from five European economies," MPRA Paper 36282, University Library of Munich, Germany.
    6. Chafaï, Djalil, 2010. "The Dirichlet Markov Ensemble," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 555-567, March.
    7. Mariolis, Theodore & Tsoulfidis, Lefteris, 2010. "Eigenvalue distribution and the production price-profit rate relationship in linear single-product systems: theory and empirical evidence," MPRA Paper 43716, University Library of Munich, Germany.

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