The rate of convergence for spectra of GUE and LUE matrix ensembles |
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| Authors: | Friedrich Götze Alexander Tikhomirov |
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| Institution: | (1) Faculty of Mathematics, University of Bielefeld, Germany;(2) Faculty of Mathematics, Syktyvkar State University, Syktyvkar, Russia;(3) Department of Mathematics, IMM of the Ural Branch RAS, Syktyvkar, Russia |
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| Abstract: | We obtain optimal bounds of order O(n
−1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution
functions of random matrices from the GUE and LUE, respectively.
Research supported by the DFG-Forschergruppe FOR 399/1. Partially supported by INTAS grant N 03-51-5018, by RFBR grant N 02-01-00233,
and by RFBR-DFG grant N 04-01-04000. |
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| Keywords: | Random matrix theory Gaussian unitary ensemble Laguerre unitary ensemble Stein’ s method semicircle law Marchenko-Pastur law |
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