Topics in Probability (Random Matrices)
Lecturers and Teaching Assistants
Prof. Ofer Zeitouni
Course Schedule and Location
Tuesday, 09:15 - 11:00, Ziskind, Rm 155
Field of Study, Course Type and Credit Points
Mathematics and Computer Science: Lecture; Elective; 2.00 points
Attendance and participation
Estimated Weekly Independent Workload (in hours)
The course will discuss the theory of random matrices, their spectra and spacing distributions. Topics to be covered include:
- Convergence of empirical measure of eigenvalues for matrices with independent entries - combinatorial and analytical techniques.
- Applications of concentration inequalities.
- Joint distribution of eigenvalues and the GOE/GUE/GSE
- Spacing distributions in the GOE/GUE/GSE: bulk and edge scalings, Tracy-Widom distributions, and link to Painleve equations.
- The process of eigenvalues of the GUE as a determinantal process.
- Introduction to free probability.
- Non-hermitian matrices and perturbations.
Upon successful completion of the course, the students will be able to:
Acquire knowledge in the basics of RMT.
Anderson, Guionnet, Zeitouni "An introduction to random matrices"
Tao "Topics in random matrices"