Summer Semester 2020
News: Second email has been sent to those who contacted me about this course. It contains a zoom link to the first lecture. If you have not received any emails from me -- please contact me again ( I might have missed your email ?). If you are interested in the course but have not written me an email yet -- please do not hesitate to write me (links to lectures will be distributed via emails to the official uni-bonn emails).
During the first part of the course the lectures will happen online. Please consult this webpage for the general information on the course, there will be further updates related to the organisation of the process. If you are interested in the course, you can email me at "mylastname" AT iam.uni-bonn.de --- I will include you to the email list where I will also send all relevant information about the course (e.g. links to zoom meetings / online lectures -- they will not be posted here). Please use your official uni-bonn email for this.
Course: V5F2 Classical Random Matrix Ensembles
Lecturer: Alexey Bufetov
Time: Friday 2--4 pm (1 lecture per week). First lecture is on 24 April.
Prerequisites: Basic Probability (e.g. central limit theorem), Basic Analysis ( e.g. change of variables in multi-dimensional integrals), Basic Linear Algebra (e.g. unitary matrices)
The course is devoted to the study of classical random matrix ensembles: Gaussian Unitary Ensemble and Circular Unitary Ensemble. The main goal is to derive the distributions of eigenvalues of these random matrices, and find its asymptotic behavior (as the size of the matrix tends to infinity) in several different limit regimes. If time permits, we will also briefly discuss a couple of the following related topics: Dyson Brownian Motion / Gaussian Orthogonal Ensemble / Ginibre Ensemble.
Sources:
"An Introduction to Random Matrices", G. Anderson, A. Guionnet, O. Zeitouni, available at author's webpage at http://www.wisdom.weizmann.ac.il/~zeitouni/cupbook.pdf , the plan is to cover a large part of material from Chapter 3, and Section 4.1
"Topic in Random Matrix Theory", T. Tao, available at author's webpage at https://terrytao.files.wordpress.com/2011/02/matrix-book.pdf , Section 2.6 and, if time permits, part of Sections 2.8 and 3.1