The Spectrum of Large Random Matrices (MATH231B, Spring 2012)

This course is about the asymptotics of the eigenvalues of large random matrices, focusing on Wigner-like matrices and the Gaussian Unitary Ensemble. Among the topics we touch upon are the combinatorics of certain non-crossing partitions and word graphs, concentration inequalities, the Stieltjes transform, Hermite polynomials, Fredholm determinants, Laplace asymptotic method, special functions (Airy, Painleve), and stochastic calculus.

Text (on reserve at math. library):

Supplementary lectures will provide insight on problems of current research interest beyond the scope of the text book.

Prerequisites: Some familiarity with probability theory and stochastic processes at the level of Stat310 or with measure theory at the level of Math205.

Requirement: Each registered student will present a 35min long lecture at end of the quarter on a topic in random matrices of choice.

Meeting: McCullough 126, Tu/Th 3:15-4:40 p.m. extra: McCullough 122 = Final date/time Mon 6/11, 12:15-3:15PM

Instructor: Amir Dembo, update: F 12:00-1:15, Sequoia 129, or e-mail amir@math.stanford.edu

See also seminar for current activity in related areas.

Schedule (per text book):

	4/3       Tu(2.1.1/2.1.2/2.3)         Th(2.3/2.4.1)
	4/10      Tu(2.4.2/2.5.1/2.5.2)       Th(3.1.1/3.2) 
	4/17      Tu(3.4/3.5.1)               Th(3.5.2/4.3.1)
	4/24      Tu(4.3.1/Bakry-Emery)       Th(Bakry-Emery)
	5/1       Tu(---)                     Th(---)
	5/8       Tu(Acceleration)            Th(Acceleration)
	5/15      Tu(Local-semi-circle)        Th(st:heavy-tail)
	5/22      Tu(Local-semi-circle)            Th(---)
	5/29      Tu(Comparison)              Th(Comparison)
	6/5       Tu(st:Toeplitz matrices)    Th(st:beta-ensembles) 
        6/11      Mo(st:edge scaling+sparse matrices)