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This is the repository for public materials for the MIT course 18.338, Eigenvalues of random matrices, for the Fall 2019 semester.
Steven Johnson will give an introductory tutorial on Julia on Friday September 6 from 5-7pm in room 32-141. Detailed instructions for setting up and using Julia are available at https://github.com/mitmath/julia-mit.
- Pre-course survey at www.tinyurl.com/18338survey
- Syllabus
We focus on the mathematics of random matrices - from the finite to the infinite, and beyond.
Our emphasis will be on interplay between the varying mathematical tools that have come to play in the modern understanding of random matrix theory. We will also discuss applications of random matrix techniques to problems in engineering and science.
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 familiary with numerical computing languages such as Julia, MATLAB, or Mathematica may be useful .... our primary focus will be Julia and some Mathematica.
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.
- Make usage of ApproxFun to explore the numerical computation of RMT laws with determinant approach, using (Bornermann, 2010) as a reference. A minimum deliverable includes Julia code to: 1) in the finite case, compute the exact distribution of LUE for extreme eigenvalues (min and max); 2) compute Tracy-Widom distribution (the infinite case).
| # | Day | Date | Topic | Reading | HW |
|---|---|---|---|---|---|
| 1 | Wed | 2019-09-04 | Hermite, Laguerre, Jacobi Listen to Random Matrix Theory It's trying to tell us something | [Slides][Notes] | Homework 1 |
| 2 | Mon | 2019-09-09 | Semicircle, Quartercircle, Circular and other infinite RMT Laws | ||
| 3 | Wed | 2019-09-11 | Semicircle Proof, and Random Growth Model | ||
| - | - | ------ | ------ | ----- | -- |