## Projektseminar (Functional Analysis): Topics in random matrix theory

Wintersemester 2014/15

Time and Place

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PJSE 2 std. | Di 12:05-13:35 | SR10 | 7.10 |

Topics

Ramdom matrix theory is a hot topic both in mathematics and physics with important connections
to many other areas. We will try to take a first look into this fascinating area by
reading the book Topics in random matrix theory
by Terence Tao.

Presentations

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28.10 | Concentration of measure 1 | Frieder Simon | [Tao] |

4.11 | Concentration of measure 2 | Tobias Schubhart | [Tao] |

18.11 | The central limit theorem 1 | Till Luc Lange | [Tao] |

25.11 | The central limit theorem 2 | Anna Till | [Tao] |

9.12 | The operator norm of random matrices | Hadded Zouhair | [Tao] |

16.12 | The semicircular law | Aleksey Kostenko | [Tao] |

13.1 | Gaussian unitary ensemble: distribution of eigenvalues 1 | Ira Egorova | [vM], [PS], [Tao] |

20.1 | Gaussian unitary ensemble: distribution of eigenvalues 2 | Ira Egorova | [vM], [PS], [Tao] |

27.1 | Gaussian unitary ensemble: distribution of eigenvalues 3 | Ira Egorova | [vM], [PS], [Tao] |

References:

- P. van Moerbeke, Random and Integrable Models in Mathematics and Physics, in "Random Matrices, Random Processes and Integrable Systems", J. Harnad (ed), Springer 2011
- L. Pastur and M. Shcherbina, Eigenvalue Distribution of Large Random Matrices, Amer. Math. Soc 2011
- T. Tao, Topics in random matrix theory, Amer. Math. Soc., Providence, 2013

Course assessment

Preparation and presentation of a chosen topic.

Audience

Majors in Mathematics (master program, code MANS), Physics, ...

Auf Ihr Kommen freuen sich Aleksey Kostenko und Gerald Teschl