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Operators associated with soft and hard spectral edges from unitary ensembles.

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Operators associated with soft and hard spectral edges from unitary ensembles. / Blower, Gordon.

In: Journal of Mathematical Analysis and Applications, Vol. 337, No. 1, 01.01.2008, p. 239-265.

Research output: Contribution to journalJournal articlepeer-review

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Blower, G 2008, 'Operators associated with soft and hard spectral edges from unitary ensembles.', Journal of Mathematical Analysis and Applications, vol. 337, no. 1, pp. 239-265. https://doi.org/10.1016/j.jmaa.2007.03.084

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Blower, Gordon. / Operators associated with soft and hard spectral edges from unitary ensembles. In: Journal of Mathematical Analysis and Applications. 2008 ; Vol. 337, No. 1. pp. 239-265.

Bibtex

@article{c78a5f8ec81e4418853f5d80ef52acfd,
title = "Operators associated with soft and hard spectral edges from unitary ensembles.",
abstract = "Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of integrable operators associated with soft and hard edges of eigenvalues distributions of random matrices. Such Tracy--Widom operators are realized as controllability operators for linear systems, and are reporducing kernels for weighted Hardy spaces, known as Sonine spaces. Periodic solutions of Hill's equation give a new family of Tracy--Widom type operators. This paper identifies a pair of unitary groups that satisfy the von Neumann--Weyl anti-commutation relations and leave invariant the subspaces of L^2 that are the ranges of projections given by Tracy--Widom operators for the soft edge of the unitary ensemble and hard edge of the Jacobi ensemble.",
keywords = "Random matrics, GUE, Hankel operators, Sonine spaces, Hill's equation",
author = "Gordon Blower",
note = "The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 337 (1), 2008, {\textcopyright} ELSEVIER.",
year = "2008",
month = jan,
day = "1",
doi = "10.1016/j.jmaa.2007.03.084",
language = "English",
volume = "337",
pages = "239--265",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - Operators associated with soft and hard spectral edges from unitary ensembles.

AU - Blower, Gordon

N1 - The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 337 (1), 2008, © ELSEVIER.

PY - 2008/1/1

Y1 - 2008/1/1

N2 - Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of integrable operators associated with soft and hard edges of eigenvalues distributions of random matrices. Such Tracy--Widom operators are realized as controllability operators for linear systems, and are reporducing kernels for weighted Hardy spaces, known as Sonine spaces. Periodic solutions of Hill's equation give a new family of Tracy--Widom type operators. This paper identifies a pair of unitary groups that satisfy the von Neumann--Weyl anti-commutation relations and leave invariant the subspaces of L^2 that are the ranges of projections given by Tracy--Widom operators for the soft edge of the unitary ensemble and hard edge of the Jacobi ensemble.

AB - Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of integrable operators associated with soft and hard edges of eigenvalues distributions of random matrices. Such Tracy--Widom operators are realized as controllability operators for linear systems, and are reporducing kernels for weighted Hardy spaces, known as Sonine spaces. Periodic solutions of Hill's equation give a new family of Tracy--Widom type operators. This paper identifies a pair of unitary groups that satisfy the von Neumann--Weyl anti-commutation relations and leave invariant the subspaces of L^2 that are the ranges of projections given by Tracy--Widom operators for the soft edge of the unitary ensemble and hard edge of the Jacobi ensemble.

KW - Random matrics

KW - GUE

KW - Hankel operators

KW - Sonine spaces

KW - Hill's equation

U2 - 10.1016/j.jmaa.2007.03.084

DO - 10.1016/j.jmaa.2007.03.084

M3 - Journal article

VL - 337

SP - 239

EP - 265

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -