R A N D O M M A T R I X T H E O R Y, S P R I N G 2 0 1 8
Lectures: Tuesday, 3.20pm-5pm, in Warren Weaver Hall 517.
Lecturer: Paul Bourgade. For office hours, you can set up an appointment or just drop by (Warren Weaver Hall 603).
This course will introduce techniques to understand the spectrum and eigenvectors of large random self-adjoint matrices, on both global and local scales. Topics include determinantal processes, Dyson's Brownian motion, universality for random matrices and related problems for the Riemann ζ function.
Prerequisites: Basic knowledge of linear algebra, probability theory and stochastic calculus is required.
Textbooks: There is no reference book for this course. Possible useful texts are:
Greg Anderson, Alice Guionnet and Ofer Zeitouni. An Introduction to Random Matrices.
Percy Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach.
Laszlo Erdos and Horng-Tzer Yau's lecture notes on universality for random matrices.
Laszlo Erdos, lecture notes on local laws for random matrices.
Homework: Once a month.
Grading: Based on problem sets and attendance/participation at lectures, and a blackboard exam if necessary.
A tentative schedule for this course is (click on the title for detailed content):