Universality for orthogonal and symplectic ensembles
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.)