This course is about the asymptotics of the eigenvalues of large random matrices, focusing on Wigner matrices and the Gaussian Unitary Ensemble. Among the topics we touch upon are the combinatorics of 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.
We shall follow the recent lecture notes on this subject by Andreson, Guionnet and Zeitouni (copies will be made available to students registered to this course).
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 20min lecture on Wendesday, June 1st, on a topic in random matrices of choice (organized in small groups to cover material in sufficient depth).
Meeting: Sequoia Hall 200, MW 11:00-12:30. First meeting, March 30th, 2005.
Instructor: Amir Dembo, M 3:00-4:00, Sequoia Hall 129, or e-mail amir@math.stanford.edu
See also seminar for current activity in related areas.
Schedule (per lecture notes):
3/28 M(---) W(2.1) 4/4 M(2.1) W(2.1/2.2) 4/11 M(2.3) W(2.4) 4/18 M(2.5) W(2.5/2.6) 4/25 M(3.1) W(3.3/3.4) 5/2 M(3.4/3.2/3.6) W(3.6) 5/9 M(3.5) W(3.7) 5/16 M(supplements) W(---) 5/23 M(Chatterjee) W(Paul) 5/30 M(--) W(students) F(students) 11-1pm