Spring 2021
Welcome to the Columbia Student Probability Seminar.
This semester we will be studying random matrix theory from the book An Introduction to Random Matrices
by Anderson, Guionnet and Zeitouni. Our talks this semester will be held over Zoom on Mondays from 12pm to 1pm (EST).
Email me (hindy.drillick at columbia.edu)
if you want to be added to the seminar mailing list. The website for Fall 2020 is here.
Welcome to the Columbia Student Probability Seminar. This semester we will be studying random matrix theory from the book An Introduction to Random Matrices by Anderson, Guionnet and Zeitouni. Our talks this semester will be held over Zoom on Mondays from 12pm to 1pm (EST).
Email me (hindy.drillick at columbia.edu) if you want to be added to the seminar mailing list. The website for Fall 2020 is here.
Schedule of Talks
| Date | Speaker | Title |
|---|---|---|
| January 25 | Weitao Zhu | Wigner's Semicircle Law I will speak about (real) Wigner matrices and prove Wigner semicircle law with the method of moments approach. I will also discuss how to derive a simple version of a central limit theorem for linear statistics of the eigenvalues of Wigner matrices. | February 1 | Sayan Das | Proof of Semicircle Law via Stieltjes Transform I will define the Stieltjes transformation for measures and then prove the Semicircle Law for Wigner matrices using them. |
February 8 | Hindy Drillick | Computing the Joint Distribution of Eigenvalues for the GOE |
February 15 | Zoe Himwich | Large Deviations for Random Matrices Part 1 I will discuss large deviations of the empirical measure and top eigenvalue. |
February 22 | Zoe Himwich | Large Deviations for Random Matrices Part 2 I will discuss large deviations of the empirical measure and top eigenvalue. |
March 8 | Yier Lin | Determinantal structure in GUE I will explain how to express the density of eigenvalues in GUE into a determinant and use this to calculate the moment of the empirical measure, in a non-combinatorial way. I will also present a bound on the top eigenvalue of GUE by Ledoux, if time allows. |
March 15 | Georgy Gaitsgori | Gaudin-Mehta Theorem about the Spacing Between the Eigenvalues of GUE We continue to talk about eigenvalues of GUE. I will discuss the theorem about the spacing between the eigenvalues and show three key steps how to prove it. Depending on the time, we'll try to prove the first and the second steps. |
March 22 | Hindy Drillick | Gap probabilities at Zero |
April 5 | Sayan Das | What happens at the edge of the spectrum of GUE? |