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VOL. 5 | 2009 A remark on the maximum eigenvalue for circulant matrices
Włodek Bryc, Sunder Sethuraman

Editor(s) Christian Houdré, Vladimir Koltchinskii, David M. Mason, Magda Peligrad

Abstract

We point out that the method of Davis-Mikosch [Ann. Probab. 27 (1999) 522–536] gives for a symmetric circulant n×n matrix composed of i.i.d. entries with mean 0 and finite (2+δ)-moments in the first half-row that the maximum eigenvalue is on the order $\sqrt{2n \log n}$, and the fluctuations are Gumbel.

Information

Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.60006

Digital Object Identifier: 10.1214/09-IMSCOLL512

Subjects:
Primary: 15A52

Keywords: circulant , eigenvalue , Gumbel , matrix , Maximum , random

Rights: Copyright © 2009, Institute of Mathematical Statistics

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