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The focus of this semester will be on the mathematics of random matrices - from the finite to the infinite, and beyond.
We will learn about the tools such as the Stieltjes transform, and Free Probability used to characterize infinite random matrices.
Our emphasis will be on exploring known connections between these tools (such as the combinatorial aspects of free probability) and discovering new connnections (such as between multivariate orthogonal polynomials and free cumulants of free probability).
We will also discuss applications of these techniques to problems in engineering and statistical physics.
Additional topics will be decided based on the interests of the students.
No particular prerequisites are needed though a proficiency in linear algebra and basic probability will be assumed. A familiarity with MATLAB will also be useful.
Meeting schedule and location
Time: Monday, Wednesday, 3:00 pm-4:30 pm
Location: 2-146