2006-07 Program on High Dimensional Inference and Random Matrices

Course Name: Random Matrices

Instructor Name: Jack W. Silverstein
Course Day and Time: Thursday 4:30 - 7:30, beginning Sept. 7
Room 104 NISS Building

Short Course Description:

This course is an introduction to properties of eigenvalues of classes of random matrices fundamental to several areas of application, including multivariate statistics, high energy physics, numerical analysis, and wireless communications. Most of the results are expressed in terms of limit theorems, as the dimensions of the matrices increase, the significance of which enables the understanding of spectral behavior for random matrices of large dimension. The main results to be covered will include the limiting behavior of empirical measure of the eigenvalues (law of large numbers and CLT's for linear statistics), extreme eigenvalues, distribution of largest eigenvalue, concentration inequalities and large deviation theory for the empirical measure and maximal eigenvalue. The basic mathematical tools used to prove these results will be introduced, among them being: moment method, Stieltjes transform, concentration inequalities and large deviations, and integrable systems. Lectures on applications to multivariate statistics will be included. The course will be team-taught by individuals who are renowned experts in random matrices.

Duke Course Listing STA 294.1 (please contact Margaret ([email protected]) for a permission number)

NCSU Course Listing MA/ST 810J.002

UNC Course Listing MATH/STAT 891.001 (Instructor listed as Chris Jones)

The classes are 3 credits/units at each university.

Questions about the course or the Random Matrices program should be emailed to [email protected].

Entire site © 2001-2008, Statistical and Applied Mathematical Sciences Institute. All Rights Reserved.