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Device-to-device (D2D) networks underlaying a millimeter-wave cellular network have great potential for capacity growth. Thus, it is important to characterize the outage of such a D2D link incorporating millimeter-wave propagation effects, user association rules, power control, and spatial randomness. To this end, we model the locations of cellular transmitters and receivers as homogeneous Poisson point processes and those of the D2D nodes as a Matérn cluster process, and incorporate blockages due to random objects, sectored antenna patterns, log-distance path loss, and Nakagami-m fading. Furthermore, we consider antenna gain inversion-based power control, and peak power constraints for D2D devices along with distinct path loss exponents and distinct fading severities for line-of-sight (LOS) and non-LOS scenarios. With the aid of stochastic geometry tools, we derive closed-form expressions of the …