Math 833 - Random Matrices

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.

Textbook: The course will not have an official textbook. I will post lecture notes for certain parts of the material on Canvas.

A couple of useful references:
Course Content: we (plan to) cover the following topics :

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.

Histogram of the eigenvalues of a 1000X1000 symmetric matrix with i.i.d. standard Gaussian entries:

Eigenvalues of a 1000X1000 symmetric
      matrix with i.i.d. Gaussian entries

Eigenvalues of a 1000X1000 matrix with i.i.d. Gaussian entries

Eigenvalues of a 1000X1000 matrix with
      i.i.d. Gaussian entries