#
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.)