Special software is required to use some of the files in this section: .ps.
| LEC # | TOPICS | Readings |
|---|---|---|
| 1 | Introduction | Advances in Random Matrix Theory (PDF) |
| 2 | The Hermite Ensemble: Wigner's Semi-Circle Law | Wigner's Original Paper: Wigner's Semi-Circle Law Other Derivations (PDF), Forrester's Notes (PS) |
| 3 | The Laguerre Ensemble: Marcenko-Pastur Theorem | Silverstein's Derivation: Paper 1 (PDF), Paper 2 (PDF) Jonsson's Paper: Some limit theorems for the eigenvalues of a sample covariance matrix |
| 4 | The Jacobi Ensemble: McKay's Random Graph Theorem | McKay's Paper: The expected eigenvalue distribution of a large regular graph |
| 5 | The "Semi-Circular" Element: Central Limit Theorem for Infinite Random Matrices | Speicher: Paper 1 (PDF), Paper 2 (PDF) |
| 6 | Free Cumulants in Free Probability | Speicher: Paper 1 (PDF), Paper 2 (PDF) |
| 7 | Free Cumulants in Free Probability (cont.) | Speicher: Paper 1 (PDF), Paper 2 (PDF) |
| 8 | Non-Crossing Partitions and Free Cumulants | Speicher: Paper 1 (PDF), Paper 2 (PDF) |
| 9 | Free Cumulants: The Semi-Circular and "Free Poisson" Distributions | Speicher: Paper 1 (PDF), Paper 2 (PDF) |
| 10 | Additive Free Convolution | Speicher: Paper 1 (PDF), Paper 2 (PDF) |
| 11 | The R-Transform and the Marcenko-Pastur Theorem | Speicher: Paper 1 (PDF), Paper 2 (PDF) |
| 12 | Multiplicative Free Convolution | Speicher: Paper 1 (PDF), Paper 2 (PDF) |
| 13 | The S-Transform | Speicher: Paper 1 (PDF), Paper 2 (PDF) |
| 14 | Dr. Anna Scaglione Talk | |
| 15 | Orthogonal Polynomials and the Classical Matrix Ensembles | Ioana's Paper: Matrix Models for Beta Ensembles |
| 16 | Project Progress Presentation | |
| 17 | Project Progress Presentation (cont.) | |
| 18 | Tracy Widom Distribution | Tracy-Widom's Paper: On the distribution of the largest eigenvalue in principal components analysis Per's Paper (PDF) |
| 19 | Eigenvalue Spectrum Fluctuations | Johansson's Paper 1: Shape Fluctuations and Random Matrices |
| 20 | Dr. Roland Speicher Talk | |
| 21 | Free Probability and Fluctuations | Speicher and Mingo: Paper 1 (PDF), Paper 2 (PDF) |
| 22 | Zonal Polynomials and Random Matrices | Stanley's Paper: Some combinatorial aspects of the spectra of normally distributed random matrices |
| 23 | Symmetric Group Representations and Free Probability | Phillipe Biane: Paper 1 (PS), Paper 2: Free cummulants, matrix orbits and characters of symmetric groups |
| 24 | MOPs | Ioana's Paper: MOPS: Multivariate Orthogonal Polynomials (symbolically) |
| 25 | Connections and Open Problems | Diaconis' Paper (PDF) |
| 26 | Project Presentations | |
| 27 | Project Presentations (cont.) |