Far East Journal of Theoretical Statistics
Volume 14, Issue 1, Pages 47 - 56
(September 2004)
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ON THE LIMITING SPECTRAL DISTRIBUTION FUNCTION OF LARGE DIMENSIONAL RANDOM MATRICES
Sang-IL Choi (Korea)
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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 [], 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.