18.338 Eigenvalues of Random Matrices (Spring 2016)



Semester Timeline
No. Date Topic Remarks
1 Wed Feb 3Hermite, Laguerre and Jacobi ensemble: the ubiquitous triadSyllabus
1* Fri Feb 5Spiked (deformed) Random Matrix Models11-12:30 2-139, [Donoho et al., 2013][Johnstone, 2001]
1*Fri Feb 5Optional Julia Tutorial by Steven Johnson (if possible, try the instructions)5pm, 4-270
2 Mon Feb 8Guest Lecture: Michael La Croix
3 Wed Feb 10Jacobi Ensemble: angles between subspaces, gsvd and CS decomposition[PS 1]
3* Fri Feb 12IDSS Seminar: Principla Components Analysis in Light of the Spiked Model (David Donoho)
Mon Feb 15no lecturePresidents Day
4 Tue Feb 16Semicircle, Quartercircle, Circular and other infinite RMT Laws
5 Wed Feb 17Cauchy-Binet Formula and its consequences
6 Mon Feb 22Tracy-Widom Law[PS 2]
7 Wed Feb 24Tracy-Widom Law, Fredholm Determinant and Determinantal Point Processes
8 Mon Feb 29Numerical Computation of RMT Laws (Bornemann's Toolbox)
9 Wed Mar 2Orthogonal Polynomials, Tridiagonal Matrices, Gaussian Quadratures, Lanczos and all that
10 Mon Mar 7Riemann-Hilbert problem I
11 Wed Mar 9Riemann-Hilbert problem II
12 Mon Mar 14Eigenvalue Perturbation Theory and Dyson-Brownian Motion[PS 3]
13 Wed Mar 16From Gaussian Ensembles to Stochastic Operators
Mon Mar 21no lectureSpring Break
Wed Mar 23no lectureSpring Break
14 Mon Mar 28$\beta$-ensembles and Orthogonal Polynomial Ensembles
15 Wed Mar 30Jack Polynomials, Multivariate Orthogonal Polynomials and their applications I
16 Mon Apr 4Jack Polynomials, Multivariate Orthogonal Polynomials and their applications II
17 Mon Apr 6Random Growth models, Aztec Diamond and Longest Increasing Subsequence (LIS)
18 Mon Apr 11LIS, Group Representation and Baik-Deift-Johansson theorem
19 Mon Apr 13Ghost and Shadows
* Mon Apr 18no lecturePatriots Day
20 Wed Apr 20 Free Probability I
21 Mon Apr 25 Free Probability II
22 Wed Apr 27 Free Probability III
23 Mon May 2 Project Presentation
24 Wed May 4 Project Presentation
25 Mon May 9 Project Presentation
26 Wed May 11 Project Presentation