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 2 4
Lectures: Tuesday, Thursday, 12:30-1:45pm, in Warren Weaver Hall 1302.
Lecturer: Paul Bourgade. For office hours, you can set up an appointment or just drop by (Warren Weaver Hall 629).
Course description:
This course will introduce techniques to understand the spectrum and eigenvectors of large random matrices, self-adjoint or not, 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. Lecture notes will be updated here. 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.
A tentative schedule for this course is (click on the title for detailed content):