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.)