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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. 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.
    4. 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.
    5. 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.
    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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