Universality for Laguerre type orthogonal and symplectic
ensembles at the hard edge of the spectrum

Maarten Vanlessen

Abstract: Consider the Laguerre-type weights $|x|^\alpha e^{-Q(x)}$ on $[0,\infty)$ where $Q$ denotes a polynomial with
positive leading coefficient. I will show that the local eigenvalue correlations of random matrices taken from the orthogonal
and symplectic ensembles associated to these Laguerre-type weights have universal behavior (when the size of the matrices
goes to infinity) at the hard of the spectrum. To get this result one needs the asymptotics of the corresponding orthogonal
polynomials together with Widom's formalism to express the correlation kernels for the orthogonal and symplectic ensembles
in terms of the unitary correlation kernel plus a correction term.

( Joint work with Deift, Kriecherbauer and Gioev.)