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.) |

## Calendar

## Course Info

##### Instructors

##### Departments

##### As Taught In

Fall
2004

##### Level

##### Topics

##### Learning Resource Types

*notes*Lecture Notes