Infinite Random Matrix Theory
MIT OpenCourseWare offers this advanced graduate course on the mathematics of infinite random matrices, taught through the Department of Aeronautics and Astronautics. Students learn the Stieltjes transform and Free Probability theory as tools for characterizing the limiting behavior of large random matrices, connecting to applications in signal processing, wireless communications, and high dimensional statistics. The site provides lecture notes, problem sets, and readings covering topics such as free convolution, the semicircle law, and deterministic equivalents. As with other MIT OCW offerings, all materials are free to access and there is no certificate offered. The course assumes strong prior background in linear algebra and probability, making it suited to students already comfortable with graduate level mathematics who want a rigorous treatment of random matrix asymptotics rather than an introductory survey.