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Some results on random circulant matrices

Mark W. Meckes

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Abstract

This paper considers random (non-Hermitian) circulant matrices, and proves several results analogous to recent theorems on non-Hermitian random matrices with independent entries. In particular, the limiting spectral distribution of a random circulant matrix is shown to be complex normal, and bounds are given for the probability that a circulant sign matrix is singular.

Chapter information

Source
Christian Houdré, Vladimir Koltchinskii, David M. Mason and Magda Peligrad, eds., High Dimensional Probability V: The Luminy Volume (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009), 213-223

Dates
First available in Project Euclid: 2 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1265119270

Digital Object Identifier
doi:10.1214/09-IMSCOLL514

Mathematical Reviews number (MathSciNet)
MR2797949

Zentralblatt MATH identifier
1243.60008

Subjects
Primary: 15A52
Secondary: 60F05: Central limit and other weak theorems

Keywords
random matrix circulant matrix eigenvalues

Rights
Copyright © 2009, Institute of Mathematical Statistics

Citation

Meckes, Mark W. Some results on random circulant matrices. High Dimensional Probability V: The Luminy Volume, 213--223, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2009. doi:10.1214/09-IMSCOLL514. https://projecteuclid.org/euclid.imsc/1265119270


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