Universality for orthogonal and symplectic ensembles

Percy Deift

Abstract: We show how to prove universality, in the bulk and at the edge, for orthogonal and symplectic emsembles of matrices with weights of the form exp(-V(x))dx, where V(x) is a polynomial of even degree. We use the formalism of Tracy-Widom, as developed further by Widom. The method depends on the asymptotic properties of orthogonal (rather than skew-orthogonal) polynomials and here Riemann-Hilbert/steepest -descent techniques play a key role.

(Based on joint work with Dimitri Gioev.)