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Infinite Random Matrix Theory >> Content Detail



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LEC #TOPICSReadings
1IntroductionAdvances in Random Matrix Theory (PDF)
2The Hermite Ensemble: Wigner's Semi-Circle Law
Wigner's Original Paper: Wigner's Semi-Circle Law

Other Derivations (PDF), Forrester's Notes (PS)
3The 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
4The Jacobi Ensemble: McKay's Random Graph TheoremMcKay's Paper: The expected eigenvalue distribution of a large regular graph
5The "Semi-Circular" Element: Central Limit Theorem for Infinite Random MatricesSpeicher: Paper 1 (PDF), Paper 2 (PDF)
6Free Cumulants in Free ProbabilitySpeicher: Paper 1 (PDF), Paper 2 (PDF)
7Free Cumulants in Free Probability (cont.)Speicher: Paper 1 (PDF), Paper 2 (PDF)
8Non-Crossing Partitions and Free CumulantsSpeicher: Paper 1 (PDF), Paper 2 (PDF)
9Free Cumulants: The Semi-Circular and "Free Poisson" DistributionsSpeicher: Paper 1 (PDF), Paper 2 (PDF)
10Additive Free ConvolutionSpeicher: Paper 1 (PDF), Paper 2 (PDF)
11The R-Transform and the Marcenko-Pastur TheoremSpeicher: Paper 1 (PDF), Paper 2 (PDF)
12Multiplicative Free ConvolutionSpeicher: Paper 1 (PDF), Paper 2 (PDF)
13The S-TransformSpeicher: Paper 1 (PDF), Paper 2 (PDF)
14Dr. Anna Scaglione Talk
15Orthogonal Polynomials and the Classical Matrix EnsemblesIoana's Paper: Matrix Models for Beta Ensembles
16Project Progress Presentation
17Project Progress Presentation (cont.)
18Tracy Widom DistributionTracy-Widom's Paper: On the distribution of the largest eigenvalue in principal components analysis

Per's Paper (PDF)
19Eigenvalue 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

20Dr. Roland Speicher Talk
21Free Probability and FluctuationsSpeicher and Mingo: Paper 1 (PDF), Paper 2 (PDF)
22Zonal Polynomials and Random MatricesStanley's Paper: Some combinatorial aspects of the spectra of normally distributed random matrices
23Symmetric Group Representations and Free ProbabilityPhillipe Biane: Paper 1 (PS), Paper 2: Free cummulants, matrix orbits and characters of symmetric groups
24MOPsIoana's Paper: MOPS: Multivariate Orthogonal Polynomials (symbolically)
25Connections and Open ProblemsDiaconis' Paper (PDF)
26Project Presentations
27Project Presentations (cont.)

 








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