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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo


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Volume 8, Issue 4

Issues

Volume 13 (2015)

Characteristic polynomials of sample covariance matrices: The non-square case

Holger Kösters
Published Online: 2010-07-24 | DOI: https://doi.org/10.2478/s11533-010-0035-2

Abstract

We consider the sample covariance matrices of large data matrices which have i.i.d. complex matrix entries and which are non-square in the sense that the difference between the number of rows and the number of columns tends to infinity. We show that the second-order correlation function of the characteristic polynomial of the sample covariance matrix is asymptotically given by the sine kernel in the bulk of the spectrum and by the Airy kernel at the edge of the spectrum. Similar results are given for real sample covariance matrices.

MSC: 15A52

Keywords: Random matrices; Characteristic polynomials; Bessel functions

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About the article

Published Online: 2010-07-24

Published in Print: 2010-08-01


Citation Information: Open Mathematics, Volume 8, Issue 4, Pages 763–779, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-010-0035-2.

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© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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