Course Identification

Topics in Probability (Random Matrices)
20194091

Lecturers and Teaching Assistants

Prof. Ofer Zeitouni
N/A

Course Schedule and Location

2019
First Semester
Tuesday, 09:15 - 11:00, Ziskind, Rm 155
06/11/2018

Field of Study, Course Type and Credit Points

Mathematics and Computer Science: Lecture; Elective; 2.00 points

Comments

N/A

Prerequisites

No

Restrictions

30

Language of Instruction

English

Attendance and participation

Expected and Recommended

Grade Type

Numerical (out of 100)

Grade Breakdown (in %)

100%

Evaluation Type

Final assignment

Scheduled date 1

N/A
N/A
-
N/A

Estimated Weekly Independent Workload (in hours)

3

Syllabus

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.

Learning Outcomes

Upon successful completion of the course, the students will be able to:

Acquire knowledge in the basics of RMT.

Reading List

Anderson, Guionnet, Zeitouni "An introduction to random matrices"

Tao "Topics in random matrices"

Website

N/A