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

Holger Kösters

Open Mathematics (2010)

  • Volume: 8, Issue: 4, page 763-779
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Holger Kösters. "Characteristic polynomials of sample covariance matrices: The non-square case." Open Mathematics 8.4 (2010): 763-779. <http://eudml.org/doc/269406>.

@article{HolgerKösters2010,
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.},
author = {Holger Kösters},
journal = {Open Mathematics},
keywords = {Random matrices; Characteristic polynomials; Bessel functions; random matrices; characteristic polynomials; complex sample covariance matrix; Hamiltonian matrix; real sample covariance matrix; sine kernel; spectrum; Airy kernel},
language = {eng},
number = {4},
pages = {763-779},
title = {Characteristic polynomials of sample covariance matrices: The non-square case},
url = {http://eudml.org/doc/269406},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Holger Kösters
TI - Characteristic polynomials of sample covariance matrices: The non-square case
JO - Open Mathematics
PY - 2010
VL - 8
IS - 4
SP - 763
EP - 779
AB - 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.
LA - eng
KW - Random matrices; Characteristic polynomials; Bessel functions; random matrices; characteristic polynomials; complex sample covariance matrix; Hamiltonian matrix; real sample covariance matrix; sine kernel; spectrum; Airy kernel
UR - http://eudml.org/doc/269406
ER -

References

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