18.338J | Fall 2004 | Graduate
Infinite Random Matrix Theory

Calendar

Lec # TOPICS
1 Introduction
2 The Hermite Ensemble: Wigner’s Semi-Circle Law
3 The Laguerre Ensemble: Marcenko-Pastur Theorem
4 The Jacobi Ensemble: McKay’s Random Graph Theorem
5 The “Semi-Circular” Element: Central Limit Theorem for Infinite Random Matrices
6 Free Cumulants in Free Probability
7 Free Cumulants in Free Probability (cont.)
8 Non-Crossing Partitions and Free Cumulants
9 Free Cumulants: The Semi-Circular and “Free Poisson” Distributions
10 Additive Free Convolution
11 The R-Transform and the Marcenko-Pastur Theorem
12 Multiplicative Free Convolution
13 The S-Transform
14 Dr. Anna Scaglione Talk
15 Orthogonal Polynomials and the Classical Matrix Ensembles
16 Project Progress Presentation
17 Project Progress Presentation (cont.)
18 Tracy Widom Distribution
19 Eigenvalue Spectrum Fluctuations
20 Dr. Roland Speicher Talk
21 Free Probability and Fluctuations
22 Zonal Polynomials and Random Matrices
23 Symmetric Group Representations and Free Probability
24 MOPs
25 Connections and Open Problems
26 Project Presentations
27 Project Presentations (cont.)