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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 457, Pages 276–285
(Mi znsl6446)
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This article is cited in 1 scientific paper (total in 1 paper)
A sharp rate of convergence for the empirical spectral measure of a random unitary matrix
E. S. Meckes, M. W. Meckes Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, 10900 Euclid Ave., Cleveland, Ohio 44106, U.S.A.
Abstract:
We consider the convergence of the empirical spectral measures of random $N\times N$ unitary matrices. We give upper and lower bounds showing that the Kolmogorov distance between the spectral measure and the uniform measure on the unit circle is of the order $\log N/N$, both in expectation and almost surely. This implies in particular that the convergence happens more slowly for Kolmogorov distance than for the $L_1$-Kantorovich distance. The proof relies on the determinantal structure of the eigenvalue process.
Key words and phrases:
random matrices, empirical spectral measures, determinantal point processes.
Received: 04.08.2017
Citation:
E. S. Meckes, M. W. Meckes, “A sharp rate of convergence for the empirical spectral measure of a random unitary matrix”, Probability and statistics. Part 25, Zap. Nauchn. Sem. POMI, 457, POMI, St. Petersburg, 2017, 276–285; J. Math. Sci. (N. Y.), 238:4 (2019), 530–536
Linking options:
https://www.mathnet.ru/eng/znsl6446 https://www.mathnet.ru/eng/znsl/v457/p276
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Abstract page: | 74 | Full-text PDF : | 30 | References: | 22 |
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