Advances in millimeter-wave (mmW) communication open up a vast frequency band, from 30 - 300 GHz, for use in mobile communication systems. However, these new frequencies exhibit highly variable and intermittent channel characteristics. In this work, we investigate the impact of diverse mmW channel statistics on the limit and the rate at which the achievable rates converge to the infinite bandwidth capacity. In particular, we first identify the optimal power allocation algorithm, and investigate the behavior of the capacity both asymptotically and at finite number of channels. Then, we propose a suboptimal algorithm that achieves asymptotic optimality and is tractable for analysis, and analyze the convergence rate of the achievable rate under this algorithm. Analytical findings are supported by numerical investigations in realistic communication scenarios.