Prof. Dr. Roland Speicher
Felix Leid
Random matrices
(Winter Semester 2019/20)Lecture Announcement
The lectures will be given in English.
News
 Due to the spread of SARSCoV2, the university is in emergency operation (link).
The examinations for this course will be delayed by at least four weeks.  There is now a pdfversion of the lecture notes
Lectures
 Mon 12:00  13:30, Thu 10:15  11:45, lecture Hall IV, building E2.4
 The lecture is taped and the recordings will be available on our video portal.
 The slides of the first lecture are online available.
 The slides of the second lecture are online available.
Handwritten Notes
 Chapter 1
 Chapter 2
 Chapter 3
 Chapter 4
 Chapter 5
 Chapter 6
 Chapter 7
 Chapter 8
 Chapter 9
 Chapter 10
 Chapter 11
 Chapter 12
 Chapter 13
Course description
Random matrices are matrices where the entries are chosen randomly. Surprisingly, it turns out that manyquestions on random matrices, in particular on the structure of their eigenvalues, has a deterministic answer
when the size of the matrices tends to infinitiy. During the last few decades random matrix theory has become
a centrepiece of modern mathematics, with relations to many different mathematical fields, as well as
applications in applied subjects like wireless communications, data compression or financial mathematics.
The course will give an introduction into the theory of random matrices and will cover subjects like:
 examples of random matrix ensembles (GUE, Wigner matrices, Wishart matrices)
 combinatorial and analytical methods
 concentration phenomena in high dimensions
 computational methods
 Wigner's semicircle law
 statistics of largest eigenvalue and TracyWidom distribution
 determinantal processes
 statistics of longest increasing subsequence
 free probability theory
 universality
 nonhermitian random matrices and circular law
Prerequisites
Prerequisites are the basic courses on Analyis and Linear Algebra. In particular, knowledge on measure andintegration theory on the level of our Analysis 3 classes is assumed.
Background on stochastics is helpful, but not required.
Exam
In order to obtain the credit points for this course, you must actively take part at the exercise sessions and obtain 50% of the total of all points on the exercise sheets. You will then be permitted to take part at the oral exams at the end of the term which are the basis for your grade.Excercises
Tutor: Moritz SpeicherMail : mobo8[at]gmx.de
Date : Thu 14  16
Place: Room 016 (SR 4), Building E2.5
Assignments
 Assignment 01
 Assignment 02
 Assignment 03
 Assignment 04
 Assignment 05
 Assignment 06
 Assignment 07
 Assignment 08
 Assignment 09
 Assignment 10
 Assignment 11
Literature
Semesterapparat
Publications
 Gernot Akemann, Jinho Baik, Philippe Di Francesco,
Oxford Handbooks in Mathematics, 2011,
The Oxford Handbook of Random Matrix Theory  Greg Anderson, Alice Guionnet, Ofer Zeitouni,
Cambridge University Press 2010,
An Introduction to Random Matrices  Zhidong Bai, Jack Silverstein,
SpringerVerlag 2010,
Spectral Analysis of Large Dimensional Random Matrices  Percy Deift,
Courant Lecture Notes 3, Amer. Math. Soc. 1999,
Orthogonal Polynomials and Random Matrices: A RiemannHilbert Approach  Percy Deift, Dimitri Gioev,
Courant Lecture Notes 18, Amer. Math. Soc. 2009,
Random Matrix Theory: Invariant Ensembles and Universality  Alan Edelman, Raj Rao,
Acta Numer. 14 (2005), 233297,
Random matrix theory  Alan Edelman, Raj Rao,
Found. Comput. Math. 8 (2008), 649702,
The polynomial method for random matrices  Alice Guionnet,
SpringerVerlag 2009,
Large Random Matrices: Lectures on Macroscopic Asymptotics  Madan Lal Mehta,
Elsevier Academic Press 2004,
Random Matices  James Mingo, Roland Speicher,
SpringerVerlag, 2017,
Free Probability and Random Matrices  Alexandru Nica, Roland Speicher,
Cambridge University Press 2006,
Lectures on the Combinatorics of Free Probability  Antonia Tulino, Sergio VerdÃº,
Found. Trends Comm. Information Theory 1 (2004), 1182,
Random matrix theory and wireless communication
Other lectures and lecture notes on random matrices
 Lecture notes from summer 2018.
 Lecture by Prof. Dr. Folkmar Bornemann, TU MÃ¼nchen, summer 2011

Lecture by Alan Edelman, MIT, spring 2018
 Lecture notes by Todd Kemp, UC San Diego, fall 2013
 Lecture notes by PerOlof Persson
Updated: 11 July 2019 by Tobias Mai