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Distribution of Subdominant Eigenvalues of Random Matrices

G. Goldberg, P. Okunev, M. Neumann (neumann@math.uconn.edu) and H. Schneider
Additional contact information
G. Goldberg: Programming Recourses Company
P. Okunev: University of Connecticut
M. Neumann: University of Connecticut
H. Schneider: University of Wisconsin

Methodology and Computing in Applied Probability, 2000, vol. 2, issue 2, 137-151

Abstract: 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.

Keywords: random matrices; eigenvalues; stochastic matrices (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (8)

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DOI: 10.1023/A:1010093922183

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