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Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices

โœ Scribed by J.W. Silverstein; S.I. Choi

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
588 KB
Volume
54
Category
Article
ISSN
0047-259X

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Let \(X\) be \(n \times N\) containing i.i.d. complex entries with \(\mathbf{E}\left|X_{11}-\mathbf{E} X_{11}\right|^{2}=1\), and \(T\) an \(n \times n\) random Hermitian nonnegative definite, independent of \(X\). Assume, almost surely, as \(n \rightarrow \infty\), the empirical distribution functi

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A stronger result on the limiting distribution of the eigenvalues of random Hermitian matrices of the form \(A+X T X^{*}\), originally studied in Marcenko and Pastur, is presented. Here, \(X(N \times n), T(n \times n)\), and \(A(N \times N)\) are independent, with \(X\) containing i.i.d. entries hav