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):
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 email@example.com
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)