On the proof of universality for orthogonal and symplectic ensembles in random matrix theory
Ovidiu Costin, Percy Deift, Dimitri Gioev
Abstract
We give a streamlined proof of a quantitative version of a result from [DG1] which is crucial for the proof of universality in the bulk [DG1] and also at the edge [DG2] for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information on a certain ratio of the beta=1,2,4 partition functions for log gases.
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