Random Matrices and Universality II
Spring term 2020
We continue the spectral analysis of random matrices from the course Random matrices and universality I of the Winter term 2019. The main goal of the course is understanding several instances of the universality phenomenon in random matrix theory. This is, that many microscopic statistics of a random matrix, i.e. statistics on the scale of the typical eigenvalue fluctuations, do not depend on fine details of the random matrix ensemble but solely its basic symmetry type. The basic tools will be Green function comparison theorems and a detailed analysis of Dyson Brownian motion, a stochastic dynamics on the eigenvalues of a matrix.
Time and place
Lecture: 
Tuesday,  9:15  11:00 
Room SM17 
Exercise class: 
Tuesday,  11:15  12:00 
Room SM17 
Contents
 Bulk universality via moment matching, Green function comparison theorems.
 DysonBrownian motion.
 Edge universality via DysonBrownian motion.
Videos of the lectures
Since the course is part of the Master Class in Mathematical Physics 20192020 of the NCCR Swissmap,
the lectures are recorded and can be found in the Master Class playlist on youtube.
Direct links
1st  lecture:

March 3

Video

2nd  lecture:

March 9

Video

3rd  lecture:

March 17

Video

4th  lecture:

March 24

Video

5th  lecture:

March 31

Video

6th  lecture:

April 7

Video

7th  lecture:

April 21

Video

8th  lecture:

April 28

Video

9th  lecture:

May 5

Video

10th  lecture:

May 12

Video

11th  lecture:

May 19

Video

12th  lecture:

May 26

Video

Homework exercises
The homework exercises are posted weekly on Moodle.
Literature
 Greg W. Anderson, Alice Guionnet, Ofer Zeitouni: An Introduction to Random Matrices,
Cambridge University Press, 2010.
 Zhidong Bai, Jack W. Silverstein: Spectral Analysis of Large Dimensional Random Matrices, Springer, 2010.
 Florent BenaychGeorges, Antti Knowles: Lectures on the local semicircle law for Wigner matrices, in Advanced Topics in Random Matrices, Panoramas et Synthèses 53 (2018), Société Mathématique de France.
 Paul Bourgade: Extreme gaps between eigenvalues of Wigner matrices, 2018.
 László Erdős, HorngTzer Yau:
A Dynamical Approach to Random Matrix Theory, Courant Lecture Notes, American Mathematical Society, 2017.
 Madan Lal Mehta: Random Matrices, Elsevier Academic Press, 2004.
 Terence Tao: Topics in random matrix theory, Graduate Studies in Mathematics, vol. 132, American Mathematical Society, 2012.
 Last updated on May 27, 2020 