Prof. Dr. Roland Speicher
Dr. Marwa Banna
Ricardo Schnur
Random matrices
(Summer Semester 2018)Lecture Announcement
The default language of the course is English, unless everybody speaks German.
News
Lectures
 Tu 12.0013.30, lecture hall IV
 Fr 10.1511.45, seminar room 6
Exam
The final examination will be a written exam and will take place on Tuesday, 07 August, from 10.15  13.15 in lecture hall IV. Please be there ahead of time!Excercises
 The exercise sessions take place Mo 8.3010.00 in seminar room 10 and are held by Alexander Mang.
 Alexander offers a weekly office hour on Tu 16.0017.00 in room 317.
 Attendance of the exercise sessions is compulsory, if you miss more than 2 sessions please bring a doctor's certificate.
 Exercise sheets will be released on Friday after the lecture and are due the following Friday,
you can either hand them in before the lecture or drop them into letterbox 47.  You can hand in your solutions alone or in pairs.
 You have to obtain at least 50% of the possible points to be eligible to take the final examination.
Assignments
 Assignment 01
 Assignment 02
 Assignment 03
 Assignment 04
 Assignment 05
 Assignment 06
 Assignment 07
 Assignment 08
 Assignment 09
 Assignment 10
 Assignment 11
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.
Literature
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 by Prof. Dr. Folkmar Bornemann, TU MÃ¼nchen, summer 2011

Lecture by Alan Edelman, MIT, spring 2018
 Graduate school on random matrices, Park City Mathematics Institute, summer 2017
 Lecture notes by Todd Kemp, UC San Diego, fall 2013
 Lecture notes by PerOlof Persson
Updated: 5 September 2018 by Tobias Mai