Rate of convergence to the semi-circular law |
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| Authors: | Email author" target="_blank">F?G?tzeEmail author A?Tikhomirov |
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| Institution: | (1) Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld 1, Germany;(2) Faculty of Mathematics, Syktyvkar University, Oktjabrskyi prospekt 55, 167001 Syktyvkar, Russia |
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| Abstract: | A stochastic bound of order O
P
(n
–1/2
) for the Kolmogorov distance between the spectral distribution function of an n×n matrix from Wigner ensemble and the distribution function of the semi-circular law is obtained. The result holds assuming that the twelfth moment of the entries of the matrix is uniformly bounded.Research supported by the DFG-Forschergruppe FOR 399/1-1 ``Spektrale Analyse, Asymptotische Verteilungen und Stochastische Dynamiken'.Research supported by the DFG-Forschergruppe FOR 399/1-1 ``Spektrale Analyse, Asymptotische Verteilungen und Stochastische Dynamiken'.Partially supported by Russian Foundation for Fundamental Research Grants NN02-01-00233, 00-15-96019. Partially supported by INTAS N99-01317, DFG-RFBR N99-01-04027.
Mathematics Subject Classification (2000): 60F05 |
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| Keywords: | Independent random variables Spectral distribution Random matrix |
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