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In this paper, we derive the asymptotic statistics of mutual information for multiple-input multiple-output (MIMO) Rayleigh-fading channels in the presence of spatial fading correlation at both the transmitter and the receiver. We first introduce a class of asymptotic linear spectral statistics, called correlants, for a structured correlation matrix. The mean and variance of MIMO mutual information are then expressed in terms of the correlants of spatial correlation matrices in the asymptotic regime where the number of transmit and receive antennas tends to infinity. In particular, using Szego's theorem on the asymptotic eigenvalue distribution of Toeplitz matrices, we give examples for special classes of correlation matrices with Toeplitz structure-exponential (or Kac-Murdock-Szego), tridiagonal, and constant (or intraclass ) correlation matrices.