A Sharp Rate of Convergence for the Empirical Spectral Measure of a Random Unitary Matrix
- 作者: Meckes E.S.1, Meckes M.W.1
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隶属关系:
- Case Western Reserve University
- 期: 卷 238, 编号 4 (2019)
- 页面: 530-536
- 栏目: Article
- URL: https://bakhtiniada.ru/1072-3374/article/view/242555
- DOI: https://doi.org/10.1007/s10958-019-04255-4
- ID: 242555
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详细
We consider the convergence of the empirical spectral measures of random N × N unitary matrices. We give upper and lower bounds showing that the Kolmogorov distance between the spectral measure and uniform measure on the unit circle is of 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 L1-Kantorovich distance. The proof relies on the determinantal structure of the eigenvalue process.
作者简介
E. Meckes
Case Western Reserve University
编辑信件的主要联系方式.
Email: elizabeth.meckes@case.edu
美国, Cleveland, Ohio
M. Meckes
Case Western Reserve University
Email: elizabeth.meckes@case.edu
美国, Cleveland, Ohio
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