Math 521 - Introduction to Random Matrix Theory
Sevak Mkrtchyan
456 Herman Brown Hall
e-mail: (first name).(last name)@rice.edu
Course Description
Random matrix theory started from mathematical statistics and nuclear physics, however as a result of intensive research in the past several decades it has vastly outgrown its roots, and today it is a well developed mathematical theory with numerous applications to various branches of mathematics, including spectral theory, number theory, determinantal processes, random tilings and random partitions.
The course will be introductory and very little background knowledge will be expected. We will study fundamental results on asymptotic properties of Wigner matrices and in particular the Gaussian ensembles. Topics covered will include Wigner's semicircle law, the joint distribution of eigenvalues in the GOE and GUE, the behavior of the top eigenvalue. A substantial part of the course will be devoted to discussing the necessary background mathematics in various degrees of detail. This will include orthogonal polynomials, steepest descent method, Stieltjes transform, determinantal point processes, Fredholm determinants, sine and Airy processes, Tracy-Widom distribution and Painleve equations (very briefly). Time permitting, we will explore connections with random permutations and random surfaces.
Lectures
TuTh 01:00-02:15 PM in HBH 453
Office Hours:
Schedule in person (456 Herman Brown Hall)
Textbook
G. Anderson, A. Guionnet and O. Zeitouni: An Introduction to Random Matrices
Grades
Your grade will be based on class participation and a presentation towards the end of the semester.
Disability Support
Any student with a documented disability seeking academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All such discussions will remain as confidential as possible. Students with disabilities will need to also contact Disability Support Services in the Allen Center.
Any student with a disability requiring accommodations in this course is encouraged to contact me after class or during office hours. Additionally, students will also need to contact Disability Support Services in the Allen Center.
If you have a documented disability that will impact your work in this class, please contact me to discuss your needs. Additionally, you will need to register with the Disability Support Services Office in the Allen Center.