Maarten Vanlessen
(Katholieke Universiteit Leuven, Belgium)
Universality for Laguerre type orthogonal and symplectic ensembles at the hard edge of the spectrum
(joint work with Deift, Gioev and Kriecherbauer)
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.