UC Davis Math 280
Random Matrices
Basic information
CRN code: | 80009
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Room/Time: | 2112 MSB,
Tuesday, Thursday 10:30-11:50 a.m. |
Instructor: | Alexander Soshnikov |
Office: | 3140 MSB |
Office Hours: | by appointment
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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):