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We provide a comprehensive overview of mathematical models and analytical techniques for millimeter wave (mmWave) cellular systems. The two fundamental physical differences from conventional sub-6-GHz cellular systems are: 1) vulnerability to blocking and 2) the need for significant directionality at the transmitter and/or receiver, which is achieved through the use of large antenna arrays of small individual elements. We overview and compare models for both of these factors, and present a baseline analytical approach based on stochastic geometry that allows the computation of the statistical distributions of the downlink signal-to-interference-plus-noise ratio (SINR) and also the per link data rate, which depends on the SINR as well as the average load. There are many implications of the models and analysis: 1) mmWave systems are significantly more noise-limited than at sub-6 GHz for most parameter configurations; 2) initial access is much more difficult in mmWave; 3) self-backhauling is more viable than in sub-6-GHz systems, which makes ultra-dense deployments more viable, but this leads to increasingly interference-limited behavior; and 4) in sharp contrast to sub-6-GHz systems cellular operators can mutually benefit by sharing their spectrum licenses despite the uncontrolled interference that results from doing so. We conclude by outlining several important extensions of the baseline model, many of which are promising avenues for future research. [ABSTRACT FROM PUBLISHER]