Title: Powers of large random unitary matrices and Toeplitz determinants
Authors: Duits, Maurice ×
Johansson, Kurt #
Issue Date: Mar-2010
Publisher: American Mathematical Society
Series Title: Transactions of the American Mathematical Society vol:362 issue:3 pages:1169-1187
Abstract: 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 Szegö limit theorem for Toeplitz determinants associated to symbols depending on n in a particular way. As a consequence of this result, we find that for each fixed m in N, the
random variables Tr U^{k_j(n)}/ sqrt(min(k_j(n),n)), j=1,...,m, converge to independent standard complex normals.
ISSN: 0002-9947
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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