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Some results on random circulant matrices. (English) Zbl 1243.60008

HoudrĂ©, Christian (ed.) et al., High dimensional probability. V: The Luminy volume. Most papers based on the presentations at the conference (HDP V), Luminy, France, May 26–30, 2008. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-78-2). Institute of Mathematical Statistics Collections 5, 213-223 (2009).
Summary: 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.
For the entire collection see [Zbl 1228.60006].

MSC:

60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
60F05 Central limit and other weak theorems
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