Infinite Random Matrix Theory

Readings

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)
3	The Laguerre Ensemble: Marcenko-Pastur Theorem	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)
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 (PDF) Johansson’s Paper 2: On fluctuations of eigenvalues of random Hermitian matrices Ioana’s Paper: Eigenvalues of Hermite and Laguerre ensembles: Large Beta Asymptotics
20	Dr. Roland Speicher Talk
21	Free Probability and Fluctuations	Speicher and Mingo: Paper 1, 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
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.)