Please take note that for the first two weeks, Wednesday is now Friday meaning there will be no class on Wednesday Sept 8 nor Wednesday Sept 15th. There will however be class on Friday Sept 10 and Friday Sept 17th. No matter what classes are in 4-261 from 3 to 4:30. After the first two weeks it will be Monday and Wednesday as announced. If you can't make the two Friday's i'll try my best to make materials available.
Please share with any other students who may not have regged but you believe will enroll.
- Piazza sign-up link (lecture notes available on Piazza)
This is the repository for public materials for the MIT course 18.338, Eigenvalues of random matrices, for the Fall 2021 semester.
The class will be held at 4-261 from 3--4:30pm every Monday and Wednesday.
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. Homework will be peer graded, and we will look to a rotating student for solutions.
TBA
| # | Day | Date | Topic | Reading | HW |
|---|---|---|---|---|---|
| Wed | 8-Sep | Canceled | |||
| 1 | Fri | 10-Sep | Hermite, Laguerre and Jacobi ensemble: the ubiquitous triad | [Slides][Notes] | |
| 2 | Mon | 13-Sep | Random matrix decomposition, Cauchy-Binet Formula and infinite RMT Laws | ||
| Wed | 15-Sep | Canceled | |||
| 3 | Fri | 17-Sep | Determinantal Point Processes (DPP) I | ||
| 4 | Mon | 20-Sep | Determinantal Point Processes (DPP) II | ||
| 5 | Wed | 22-Sep | Random Growth I | ||
| 6 | Mon | 27-Sep | Random Growth II | ||
| 7 | Wed | 29-Sep | Random Growth and Aztc Diamond | ||
| 8 | Mon | 4-Oct | Longest Increasing Subsequences | ||
| 9 | Wed | 6-Oct | LIS, Group Representation, and Baik-Deift-Johansson theorem | ||
| Mon | 11-Oct | Indigineous People's Day | |||
| 10 | Wed | 13-Oct | RMT in Machine Learning (ML): DPPs | ||
| 11 | Mon | 18-Oct | Symmetric Spaces and RMT | ||
| 12 | Wed | 20-Oct | Orthogonal Polynomials, Tridiagonal Matrices, Gaussian Quadratures, Lanczos and all that | ||
| 13 | Mon | 25-Oct | Eigenvalue Perturbation Theory and Dyson-Brownian Motion I | ||
| 14 | Wed | 27-Oct | Eigenvalue Perturbation Theory and Dyson-Brownian Motion II | ||
| 15 | Mon | 1-Nov | From Gaussian Ensembles to Stochastic Operators | ||
| 16 | Wed | 3-Nov | Jack Polynomials, Multivariate Orthogonal Polynomials and their applications I | ||
| 17 | Mon | 8-Nov | Jack Polynomials, Multivariate Orthogonal Polynomials and their applications II | ||
| 18 | Wed | 10-Nov | Tracy-Widom I | ||
| 19 | Mon | 15-Nov | Tracy-Widom II | ||
| 20 | Wed | 17-Nov | Free Probability I | ||
| 21 | Mon | 22-Nov | Free Probability II | ||
| 21 | Wed | 24-Nov | Canceled for Thanksgiving travel | ||
| 22 | Mon | 29-Nov | RMT in ML: Deep Learning | ||
| 23 | Wed | 1-Dec | Project Presentation I | ||
| 24 | Mon | 6-Dec | Project Presentation II | ||
| 25 | Wed | 8-Dec | Project Presentation III |