Distribution of Subdominant Eigenvalues of Random Matrices |
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| Authors: | Goldberg G. Okunev P. Neumann M. Schneider H. |
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| Affiliation: | (1) Programming Recourses Company, Hartford, Connecticut, 06105-1990;(2) Department of Mathematics, University of Connecticut, Storrs, Connecticut, 06269–3009;(3) Department of Mathematics, University of Connecticut, Storrs, Connecticut, 06269–3009;(4) Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 |
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| Abstract: | ![]()
We mainly investigate the behavior of the subdominant eigenvalue of matrices B= (bi,j)  n,n whose entries are independent random variables with an expectation Ebi,j=1/n and with a variance n  c/n2 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. |
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| Keywords: | random matrices eigenvalues stochastic matrices |
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