Math 833 - Random Matrices

Fall 2009

Meetings: TR 9:30-10:45, Van Vleck B131
Instructor: Benedek Valkó
Office: 409 Van Vleck
Phone: 263-2782
Email: valko at math dot wisc dot edu
Office hours: Tuesday 13:30-14:30 or by appointment

I will use the class email list to send out corrections, announcements, please check your wisc.edu email from time to time.

Evaluation: Students taking the course for credit are expected to write up two or three lectures in consultation with the instructor. There will also be (non mandatory) homework exercises.

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, Dyson's beta-ensemble). 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.

The course will not have an official textbook. A couple of useful references:
Course Content: we (plan to) cover the following topics :


List of transcribers

Lecture notes

Homework problems (if you are interested...)

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