COURSE DESCRIPTION
Course Description: 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. This is a graduate course that is intended to be flexible so as to cover the backgrounds of different students. Generally grading will be based on satisfactory completion of problem sets and projects or equivalents.
RECENT UPDATE
[01.27.2012] Welcome!
[02.19.2012] In Ex8 of PSset2, the off-diagonal of a Wishart matrix should be the product of a Gaussian and a chi_m distribution, NOT a Gaussian.
[03.21.2012] The Suggested Projects List is out!
