Rate of convergence to the semi-circle law for the Deformed Gaussian Unitary Ensemble |
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| Authors: | Friedrich Götze Alexander N. Tikhomirov Dmitry A. Timushev |
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| Affiliation: | (1) Faculty of Mathematics, University of Bielefeld, Germany;(2) Faculty of Mathematics and Mechanics, St.-Petersburg State University, Russia;(3) Faculty of Mathematics, Syktyvkar State University, Russia |
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| Abstract: | It is shown that the Kolmogorov distance between the expected spectral distribution function of an n × n matrix from the Deformed Gaussian Ensemble and the distribution function of the semi-circle law is of order O(n −2/3+v ). Research supported by the DFG-Forschergruppe FOR 399/1. Partially supported by INTAS grant N 03-51-5018, by RFBF grant N 02-01-00233, by RFBR-DFG grant N 04-01-04000, by RF grant of the leading scientific schools NSh-4222.2006.1. |
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| Keywords: | Random matrix theory Deformed gaussian unitary ensemble Gaussian unitary ensemble semicircle law |
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