| 1 |
Introduction |
Advances in Random Matrix Theory (PDF) |
| 2 |
The Hermite Ensemble: Wigner's Semi-Circle Law
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Wigner's Original Paper: Wigner's Semi-Circle Law
Other Derivations (PDF), Forrester's Notes (PS) |
| 3 |
The Laguerre Ensemble: Marcenko-Pastur Theorem
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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 |
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| 15 |
Orthogonal Polynomials and the Classical Matrix Ensembles |
Ioana's Paper: Matrix Models for Beta Ensembles |
| 16 |
Project Progress Presentation |
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| 17 |
Project Progress Presentation (cont.) |
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| 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
Johansson's Paper 2: On fluctuations of eigenvalues of random Hermitian matrices
Ioana's Paper: Eigenvalues of Hermite and Laguerre ensembles: Large Beta Asymptotics
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