TITLE

On the Asymptotic Distribution of Singular Values of Powers of Random Matrices

AUTHOR(S)
Alexeev, N.; Götze, F.; Tikhomirov, A.
PUB. DATE
May 2014
SOURCE
Journal of Mathematical Sciences;May2014, Vol. 199 Issue 2, p68
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We consider powers of random matrices with independent entries. Let X, i, j ≥ 1, be independent complex random variables with E X = 0 and E| X| = 1, and let X denote an n × n matrix with | X| − X for 1 ≤ i, j ≤ n. Denote by $ s_1^{(m)}\geq \ldots \geq s_n^{(m) } $ the singular values of the random matrix $ \mathbf{W}:={n^{{-\frac{m}{2}}}}{{\mathbf{X}}^m} $ and define the empirical distribution of the squared singular values by where I denotes the indicator of an event B. We prove that the expected spectral distribution $ F_n^{(m) }(x)=\mathbf{E}\mathcal{F}_n^{(m) }(x) $ converges under the Lindeberg condition to the distribution function G( x) defined by its moments
ACCESSION #
96396476

 

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