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

Blower, Gordon (2008) Operators associated with soft and hard spectral edges from unitary ensembles. Journal of Mathematical Analysis and Applications, 337 (1). pp. 239-265. ISSN 0022-247X

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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.

Item Type: Journal Article
Journal or Publication Title: Journal of Mathematical Analysis and Applications
Additional Information: The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 337 (1), 2008, © ELSEVIER.
Uncontrolled Keywords: /dk/atira/pure/researchoutput/libraryofcongress/qa
Subjects:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 737
Deposited By: Professor Gordon Blower
Deposited On: 07 Nov 2007
Refereed?: Yes
Published?: Published
Last Modified: 21 Aug 2019 00:46
URI: https://eprints.lancs.ac.uk/id/eprint/737

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