"Everything should be made as simple as possible, but not simpler." - Albert Einstein

Seminar Announcement

Continuum limits for beta ensembles

Brian Rider, University of Colorado at Boulder.

Monday, April 6, 2009

4:00 pm, 223Weber

ABSTRACT

The beta ensembles of random matrix theory are natural generalizations of the Gaussian Orthogonal, Unitary, and Symplectic Ensembles, these classical cases corresponding to beta = 1, 2, and 4. We prove that the extremal eigenvalues for the general ensembles have limit laws described by the low lying spectrum of certain random Schroedinger operators, as conjectured by Edelman-Sutton. As a corollary, a second characterization of these laws is made the explosion probability of a simple one-dimensional diffusion. A complementary pictures is developed for beta versions of random sample-covariance matrices. (Based on work with J. Ramirez and B. Virag.)