On the Proof of Universality for Orthogonal and Symplectic Ensembles in Random Matrix Theory |
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| Authors: | Ovidiu Costin Percy Deift Dimitri Gioev |
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| Institution: | (1) Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus, OH 43210, USA;(2) Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012, USA;(3) Department of Mathematics, University of Rochester, Hylan Bldg., Rochester, NY 14627, USA |
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| Abstract: | We give a streamlined proof of a quantitative version of a result from P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) which is crucial for the proof of universality in the bulk P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) and also at the edge P. Deift and D. Gioev, {Universality at the edge of the spectrum for unitary, orthogonal
and symplectic ensembles of random matrices. Comm. Pure Appl. Math. (in press) for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information
on a certain ratio of the β=1,2,4 partition functions for log gases. |
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| Keywords: | random matrix theory universality orthogonal and symplectic ensembles partition function log gases |
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