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The statistics of the mutual information of a separately correlated Rician fading multiple-input multiple-output (MIMO) channel in the presence of multiple-access interference are addressed in this paper. The approach followed is asymptotic in the number of transmit, receive, and interfering antennas, which are all assumed to grow asymptotically large while approaching finite ratios. In this asymptotic regime: i) the mean and the variance of the mutual information are calculated; and ii) the mutual information distribution is shown to converge to the Gaussian distribution, specified completely by the mean and variance, under some mild technical conditions. The asymptotic method adopted relies on two powerful tools developed in the context of theoretical physics: the replica method and superanalysis. The former has been already successfully applied in several research studies on MIMO systems. The application of these asymptotic results takes advantage of the fact that, in spite of being developed under the assumption of an asymptotically large number of antennas, they still represent a very accurate approximation even when the number of antennas is limited to a few units, as supported by the ample set of numerical results obtained by Monte Carlo simulations and reported in this paper.