Stacked intelligent metasurface (SIM) is a promising enabler for next-generation high-capacity networks that exhibit better performance compared to its single-layer counterpart by means of just wave propagation. However, the study of ergodic mutual information (EMI) and outage probability for SIM-assisted multiple-input-multiple-output (MIMO) systems is not available in the literature. To this end, we obtain the distribution of the MI by using large random matrix theory (RMT) tools. Next, we derive a tight closed-form expression for the outage probability based on statistical channel state information (CSI). Moreover, we apply the gradient descent method for the minimization of the outage probability. Simulation results verify the analytical results and provide fundamental insights such as the performance enhancements compared to conventional MIMO systems and the single-layer counterpart. Notably the proposed optimization algorithm is faster than the alternating optimization (AO) benchmark by saving significant overhead.

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