On the Empirical Distribution of Eigenvalues of Large Dimensional Information-Plus-Noise Type Matrices
نویسندگان
چکیده
Let Xn be n×N containing i.i.d. complex entries and unit variance (sum of variances of real and imaginary parts equals 1), σ > 0 constant, and Rn an n×N random matrix independent of Xn. Assume, almost surely, as n →∞, the empirical distribution function (e.d.f.) of the eigenvalues of 1 N RnR ∗ n converges in distribution to a nonrandom probability distribution function (p.d.f.), and the ratio n N tends to a positive number. Then it is shown that, almost surely, the e.d.f. of the eigenvalues of 1 N (Rn + σXn)(Rn + σXn) ∗ converges in distribution. The limit is nonrandom and is characterized in terms of its Stieltjes transform, which satisfies a certain equation.
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