Math 590S- Introduction to Random Matrices

Updates:
Feb. 19- We'll meet in WH 100E today. Feb. 19- Homework 1 is on Blackboard, under course material.

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Schedule:
Feb. 12- Introduction. This class will be held on Zoom. The link is on Blackboard. Email me if you're not enrolled, but interested in attending.
Feb. 15- Review of Probability (Section 1.1). The plan is for this class to be in WH G002, on the first day of class, we'll discuss how it'll work for online students.
Feb. 17- Review of Linear Algebra (Section 1.3)
Feb. 19- Method of Moments Proof of Central Limit Theorem (Section 2.2.3)
Feb. 22- Method of Moments Proof of Central Limit Theorem and some other proofs (Section 2.2)
Feb. 24- The semicirular law (Section 2.4)
Feb. 26- The semicirular law (Section 2.4)
Mar. 1- Method of Moments (Section 2.4) see also Lecture 1 here
Mar. 3- Method of Moments (Section 2.4)
Mar. 5- Method of Moments (Section 2.4)
Mar. 8- Method of Moments to bound Operator Norm (Section 2.3.4)
Mar. 10- Method of Moments to bound Operator Norm (Section 2.3.4)
Mar. 12- Stieljes Transform (Section 2.4.3 and 2.4 of Intoduction to Random Matrices)
Mar. 15- Stieljes Transform (Section 2.4.3)
Mar. 17- Rejuvenation Day
Mar. 19- Stieljes Transform (Section 2.4)
Mar. 22- Free Probability (Section 2.5)
Mar. 24- Free Probability (Section 2.5)
Mar. 26- Free Probability (Section 2.5)
Mar. 29- GUE (Section 2.6.1 and 2.6.4)
Mar. 31- GUE (Section 2.6.1 and 2.6.4)
Apr. 2- GUE (Section 2.6.1 and 2.6.4)
Apr. 5- GUE (Section 2.6.1 and 2.6.4)
Apr. 7- Tridiagonal Random Matrices (Section 2.6.5)
Apr. 9- Operator Norm (Section 2.3)
Apr. 12- Least Singular value (Section 2.7 - there are lots of typos these notes are better: Least singular value )
Apr. 14- Least Singular value
Apr. 16- Least Singular value
Apr. 19- Least Singular value
Apr. 21- Circular Law (Section 2.8)
Apr. 23- Circular Law (Section 2.8)
Apr. 26- Circular Law (Section 2.8)
Apr. 28- Circular Law (Section 2.8)
Apr. 30- Circular Law (Section 2.8)
May 3- Brownian Motion (Section 3.1)
May 5- Dyson Brownian Motion (Section 3.1)
May 7- Dyson Brownian Motion (Section 3.1)
May 10- Principal Component Analysis

Homework:

Homework 1 - On Blackboard
Homework 2 - Exercise 2.1.18 from An Introduction to Random Matrices Due March 19
Homework 3 - On Blackboard