Universality of the Stochastic Airy Operator

Source abstract

Abstract We introduce a new method for studying universality of random matrices. Let T n be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potential. We show that after scaling, T n converges to the stochastic Airy operator. In particular, the top edge of the Dyson beta ensemble and the corresponding eigenvectors are universal. As a byproduct, these ideas lead to conjectured operator limits for the entire family of soft edge distributions.© 2015 Wiley Periodicals, Inc.