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Powers of large random unitary matrices and toeplitz determinants
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2943-7006
2010 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 362, no 3, 1169-1187 p.Article in journal (Refereed) Published
Abstract [en]

We study the limiting behavior of Tr U-k(n), where U is an n x n random unitary matrix and k(n) is a natural number that may vary with n in an arbitrary way. Our analysis is based on the connection with Toeplitz determinants. The central observation of this paper is a strong Szego limit theorem for Toeplitz determinants associated to symbols depending on 71 in a particular way. As a consequence of this result, we find that for each fixed m is an element of N, the random variables Tr U-kj(n)/root min(k(j)(n),n), j = 1,..., m, converge to independent standard complex normals.

Place, publisher, year, edition, pages
2010. Vol. 362, no 3, 1169-1187 p.
Keyword [en]
classical compact-groups, linear statistics, eigenvalues, behavior
National Category
URN: urn:nbn:se:kth:diva-19264DOI: 10.1090/S0002-9947-09-04542-5ISI: 000275017000003ScopusID: 2-s2.0-77950870965OAI: diva2:337311
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2012-04-14Bibliographically approved

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