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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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Vol. 5 • 1 January 2009