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The limiting behavior, as n → ∞ with n/N approaching a positive constant, of functionals of the eigenvalues of B n , where each is given equal weight, is studied. Due to the limiting behavior of the empirical spectral distribution of B n , it is known that these linear spectral statistics converges a.s. to a nonrandom quantity. This paper shows their rate of convergence to be 1/n by proving, after proper scaling, that they form a tight sequence. Moreover, if EX 2 11 = 0 and E|X 11 | 4 = 2, or if X 11 and T n are real and EX 4 11 = 3, they are shown to have Gaussian limits.

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