Perturbed Toeplitz operators and radial determinantal processes

Torsten Ehrhardt; Brian Rider

Annales de l'I.H.P. Probabilités et statistiques (2013)

  • Volume: 49, Issue: 4, page 934-960
  • ISSN: 0246-0203

Abstract

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We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criterion for a central limit theorem to hold for angular statistics of the points. The proof exploits an exact formula relating the generating function of such statistics to the determinant of a perturbed Toeplitz matrix.

How to cite

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Ehrhardt, Torsten, and Rider, Brian. "Perturbed Toeplitz operators and radial determinantal processes." Annales de l'I.H.P. Probabilités et statistiques 49.4 (2013): 934-960. <http://eudml.org/doc/272031>.

@article{Ehrhardt2013,
abstract = {We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criterion for a central limit theorem to hold for angular statistics of the points. The proof exploits an exact formula relating the generating function of such statistics to the determinant of a perturbed Toeplitz matrix.},
author = {Ehrhardt, Torsten, Rider, Brian},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random matrices; determinantal processes; Toeplitz operators; Szegö–Widom limit theorem; Szegő-Widom limit theorem},
language = {eng},
number = {4},
pages = {934-960},
publisher = {Gauthier-Villars},
title = {Perturbed Toeplitz operators and radial determinantal processes},
url = {http://eudml.org/doc/272031},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Ehrhardt, Torsten
AU - Rider, Brian
TI - Perturbed Toeplitz operators and radial determinantal processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2013
PB - Gauthier-Villars
VL - 49
IS - 4
SP - 934
EP - 960
AB - We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criterion for a central limit theorem to hold for angular statistics of the points. The proof exploits an exact formula relating the generating function of such statistics to the determinant of a perturbed Toeplitz matrix.
LA - eng
KW - random matrices; determinantal processes; Toeplitz operators; Szegö–Widom limit theorem; Szegő-Widom limit theorem
UR - http://eudml.org/doc/272031
ER -

References

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