Math 8660: Random Matrix Theory

Fall 2019

Welcome to the course webpage!

Course Instructor: Arnab Sen
Office: 238 Vincent Hall

Class time: MW 9:45-11:00am
Location: Vincent Hall 20
Office hours: After lecture or by appointment.

Course Description: This course is an introduction to random matrix theory. Our main focus will be to understand the spectrum and eigenvector of large random self-adjoint matrices (Gaussian ensembles, Wigner matrices etc.) on both local and global scales. In the final part of the course, we will study some spectral properties of the adjacency matrices of large sparse random graphs. We plan to cover the following topics:

Prerequisite: No prior knowledge in random matrix theory is required but students should be comfortable with linear algebra and basic probability theory.

Evaluation: The final grade will be based on a couple of homework assignments and a presentation. There is no final exam in the course.

This course will not have an official textbook. But the following references will be useful:

1. An Introduction to Random Matrices (available online) by Greg Anderson, Alice Guionnet and Ofer Zeitouni.
2. Topics in Random Matrix Theory (available online) by Terry Tao.
3. Lecture notes on Universality for random matrices and Log-gases by Laszlo Erdos.
4. Lecture notes on Spectrum of random graphs by Charles Bordenave.
5. Zeros of Gaussian Analytic Functions and Determinantal Point Processes. (available online) by J. B. Hough, M. Krishnapur, Y. Peres and B. Virag.
6. Large random matrices: lectures on macroscopic asymptotics. Lectures from the 36th Probability Summer School held in Saint-Flour, 2006 by Alice Guionnet.
7. Lectures on the local semicircle law for Wigner matrices by Benaych-Georges and Knowles.

Homework 1 (Due on 10/30)
Homework 2 (Due on 11/25)

Possible papers for presentations (in not any particular order):

Topics covered: