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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):

- Anderson, Guionnet and Zeitouni, An introduction to random matrices.

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)