Course Description

This is a short introductory course on random matrices. We will start to derive the semicircle law for Winger matrices and prove the local semicircle law. After that, we will discuss the Dyson Brownian motions and its connection to randommatrices. These tools will be used to prove the universality of bulk and edge distributions for Wigner matrices.

If time permitted, we will discuss the sparse matrices and d-regular graphs. We will need to use Ito’s formula when dealing with Dyson Brownian motions. Besides that, the prerequisite is just basics of real analysis and probability theory.

Schedule

Monday, June 29, July 6 & 13

10:00 – 11:00   First Talk

11:00 – 11:30   Tea Break

11:30 – 12:30   Second Talk

12:30 – 14:30   Lunch

14:30 – 16:00   Discussion

Videos:
(1) Jun. 29
(2) Jun. 29
(3) Jul. 6
(4) Jul. 6