Abstract: Let be i.i.d. real-valued random
variables with For each positive integer m,
let where and as and let be an symmetric nonnegative definite
random matrix independent of the
’s. The limiting spectral distribution of studied in Marcenko and Pastur [Math.
USSR-Sbornik 1(4) (1967), 457-483], is derived. Using the Stieltjes transform, it is
shown that the limiting distribution has a continuous derivative away from zero.
In the present paper, it is derived that the limiting density function is
analytic whenever it is positive.
Keywords and phrases: eigenvalues of random matrices, spectral distribution, Stieltjes transform.
