18.338J | Fall 2004 | Graduate
Infinite Random Matrix Theory

Lecture Notes

LEC # TOPICS LECTURE NOTES SUPPORTING FILES
2 The Hermite Ensemble: Wigner’s Semi-Circle Law

Histogramming (PDF)

Experiments with the Classical Ensembles (PDF)

Histogramming

bellcurve.m (M)  
histn.m (M)  
momwigner.m (M)

Experiments with the Classical Ensembles

wigner.m (M)  
wishart.m (M)  
manova.m (M)  
wigneredf.m (M)  
wishartedf.m (M)  
manovaedf.m (M)  
classicexpt.m (M)

3 The Laguerre Ensemble: Marcenko-Pastur Theorem The Stieltjes Transform Based Approach (PDF) (Courtesy of Raj Rao. Used with permission.)  
5 The “Semi-Circular” Element: Central Limit Theorem for Infinite Random Matrices Tridiagonal Matrices, Orthogonal Polynomials and the Classical Random Matrix Ensembles (PDF) (Courtesy of Brian Sutton. Used with permission.) trijacobi.m (M)
6 Free Cumulants in Free Probability

Essentials of Finite Random Matrix Theory (PDF)

Numerical Methods in Random Matrices (PDF) (Courtesy of Per-Olof Persson. Used with permission.)

Essentials of Finite Random Matrix Theory

jsymeig.m (M)

7 Free Cumulants in Free Probability (cont.) Project Ideas (PDF)