**Spring 2019**

**Meetings:** MWF 8:50-9:55, Van Vleck ~~B325~~**
B119**

**Instructor:** Benedek Valkó

**Office:** 409 Van Vleck

**Office hours:** W 11-12 or by appointment

Course description:

The course is an introduction to random matrix theory. We will
cover results on the asymptotic properties of various random
matrix models (Wigner matrices, Gaussian ensembles,
beta-ensembles). We will investigate the limit of the empirical
spectral measure both on a global and local scale.

**Prerequisites:** Basics in probability theory and linear
algebra. Some knowledge of stochastic processes will also be
helpful.

A couple of useful references:

- M. Mehta: Random Matrices
- P.A. Deift: Orthogonal polynomials and random matrices: a Riemann-Hilbert approach.
- P. Forrester: Log-gases and Random matrices
- G. Anderson, A. Guionnet and O. Zeitouni: An Introduction to
Random Matrices

available from the O. Zeitouni's webpage - Z. Bai, J. W. Silverstein: Spectral Analysis of Large Dimensional Random Matrices
- A. Guionnet: various lecture notes available from the author's webpage
- Lecture notes from various authors:

- Terence Tao
- Fraydoun Rezakhanlou
- Manjunath Krishnapur
- Math
833 - 2009 Fall (notes taken by students)

- Wigner's semicircle law
- Exact computation of joint eigenvalue densities (Gaussian ensembles, Ginibre ensemble)
- Tridiagonal representation of the Gaussian beta-ensemble
- Bulk and edge scaling limit for the eigenvalue process of the Gaussian Unitary Ensemble
- Operator level scaling limits of beta-ensembles

**Evaluation:**

The final grade will be based
on homework assignments. The assignments will be posted on the
Canvas page of the course. There is no final exam in the course.