16.394
Infinite Random Matrix Theory
Fall 2004
Topics
- Introduction
- The Hermite Ensemble: Wigner’s Semi-Circle Law
- The Laguerre Ensemble: Marcenko-Pastur Theorem
- The Jacobi Ensemble: McKay’s Random Graph Theorem
- The “Semi-Circular” Element: Central Limit Theorem for Infinite Random Matrices
- Free Cumulants in Free Probability
- Free Cumulants in Free Probability (cont.)
- Non-Crossing Partitions and Free Cumulants
- Free Cumulants: The Semi-Circular and “Free Poisson” Distributions
- Additive Free Convolution
- The R-Transform and the Marcenko-Pastur Theorem
- Multiplicative Free Convolution
- The S-Transform
- Dr. Anna Scaglione Talk
- Orthogonal Polynomials and the Classical Matrix Ensembles
- Project Progress Presentation
- Project Progress Presentation (cont.)
- Tracy Widom Distribution
- Eigenvalue Spectrum Fluctuations
- Dr. Roland Speicher Talk
- Free Probability and Fluctuations
- Zonal Polynomials and Random Matrices
- Symmetric Group Representations and Free Probability
- MOPs
- Connections and Open Problems
- Project Presentations
- Project Presentations (cont.)
Readings
Sources
- Course catalogue ↗Historical OpenCourseWare
- MIT OCW calendar ↗
- MIT OCW readings ↗
- MIT OCW syllabus ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.