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Distribution of Subdominant Eigenvalues of Random Matrices (2000)

Goldberg, G. ; Okunev, P. ; Neumann, M. ; [et al.]

Springer

Methodology and computing in applied probability 2 (2000), S. 137-151

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ISSN: 1387-5841

Keywords: random matrices ; eigenvalues ; stochastic matrices

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1010093922183

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