UC Davis Math 280
Random Matrices

Basic information

CRN code: 80009
Room/Time: 2112 MSB, Tuesday, Thursday 10:30-11:50 a.m.
Instructor: Alexander Soshnikov
Office: 3140 MSB
Office Hours: by appointment
E-mail: soshniko@math.ucdavis.edu
 
Grading: Class Attendance and Small Project (please discuss with the instructor)
 

Syllabus and text

Textbooks/ Notes:

Topics in Random Matrix Theory by Terence Tao

"An Introduction to Random Matrices" , by G.W Anderson, Alice Guionnet, and Ofer Zeitouni

pdf file of the book available on Ofer Zeitouni's web site

Lectures:

Lecture 1 (December 10, 2014):

Introduction. Connections between Random Matrices and Other Areas of Mathematics (Number Theory, Combinatorics, Representation Theory).

Lecture 2 (January 13, 2015):

Gaussian Ensembles of Random Matrices. Joint Probability Density of Eigenvalues.

Lecture 3 (January 15):

Gaussian Ensembles. k-Point Correlation Functions.

Lecture 4 (January 20):

Orthogonal Polynomials.

Lecture 5 (January 22):

Dyson-Mehta Lemma. Determinantal Ensembles.

Lecture 6 (January 27):

Wigner Random Matrices.

Lecture 7 (January 29):

Wigner Semicircle Law.

Lecture 8 (February 3):

Wigner Semicircle Law. Method of Moments.

Lecture 9 (February 5):

Resolvent Technique.

Lecture 10 (February 10):

Resolvent Technique.

Lecture 11 (February 12):

Poincare Inequality.

Lecture 12 (February 17):

Lecture 13 (February 19):

Lecture 14 (February 24):

Lecture 15 (February 26):

Lecture 16 (March 3):

Lecture 17 (March 5):

Lecture 18 (March 10):

Lecture 19 (March 12):