Prof. Dr. Roland Speicher
Random matrices(Winter Semester 2019/20)
The lecture will be given in English.
- There have been a typpo in the exercises, check out the corrected version.
- The deadline for the second exercise sheet has been extended until Mon, 03.11.2019
- The course will be taped, you can find the recordings here.
- 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.
Course descriptionRandom matrices are matrices where the entries are chosen randomly. Surprisingly, it turns out that many
questions 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 Tracy-Widom distribution
- determinantal processes
- statistics of longest increasing subsequence
- free probability theory
- non-hermitian random matrices and circular law
PrerequisitesPrerequisites are the basic courses on Analyis and Linear Algebra. In particular, knowledge on measure and
integration theory on the level of our Analysis 3 classes is assumed.
Background on stochastics is helpful, but not required.
ExamIn 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.
ExcercisesTutor: Moritz Speicher
Mail : mobo8[at]gmx.de
Date : Thu 14 -- 16
Place: Room 016 (SR 4), Building E2.5
- 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,
Spectral Analysis of Large Dimensional Random Matrices
- Percy Deift,
Courant Lecture Notes 3, Amer. Math. Soc. 1999,
Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert 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), 233-297,
Random matrix theory
- Alan Edelman, Raj Rao,
Found. Comput. Math. 8 (2008), 649-702,
The polynomial method for random matrices
- Alice Guionnet,
Large Random Matrices: Lectures on Macroscopic Asymptotics
- Madan Lal Mehta,
Elsevier Academic Press 2004,
- James Mingo, Roland Speicher,
Free Probability and Random Matrices
- Alexandru Nica, Roland Speicher,
Cambridge University Press 2006,
Lectures on the Combinatorics of Free Probability
- Antonia Tulino, Sergio Verdú,
Found. Trends Comm. Information Theory 1 (2004), 1-182,
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 München, summer 2011
Lecture by Alan Edelman, MIT, spring 2018
- Lecture notes by Todd Kemp, UC San Diego, fall 2013
- Lecture notes by Per-Olof Persson
Updated: 11 July 2019 by Tobias Mai