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On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices

✍ Scribed by J.W. Silverstein; Z.D. Bai

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

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✦ Synopsis

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 having finite second moments, (T) is diagonal with real (diagonal) entries, (A) is Hermitian, and (n / N \rightarrow c>0) as (N \rightarrow \infty). Under additional assumptions on the eigenvalues of (A) and (T), almost sure convergence of the empirical distribution function of the eigenvalues of (A+X T X^{}) is proven with the aid of Stieltjes transforms, taking a more direct approach than previous methods.
c. 1995 Academic Press. Inc

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