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Contribution Details

Type Book Chapter
Scope Discipline-based scholarship
Title Limit Operators for Circular Ensembles
Organization Unit
Authors
  • Kenneth Maples
  • Joseph Najnudel
  • Ashkan Nikeghbali
Editors
  • Nalini Anantharaman
  • Ashkan Nikeghbali
  • Michael Th Rassias
Item Subtype Original Work
Refereed Yes
Status Published in final form
Language
  • English
Booktitle Frontiers in Analysis and Probability : In the Spirit of the Strasbourg-Zürich Meetings
ISBN 978-3-030-56408-7
Number 145
Place of Publication Cham
Publisher Springer
Page Range 327 - 369
Date 2020
Date Annual Report 2020
Abstract Text It is known that a unitary matrix can be decomposed into a product of reflections, one for each dimension, and that the Haar measure on the unitary group pushes forward to independent uniform measures on the reflections. We consider the sequence of unitary matrices given by successive products of random reflections. In this coupling, we show that powers of the sequence of matrices converge in a suitable sense to a flow of operators, which acts on a random vector space. The vector space has an explicit description as a subspace of the space of sequences of complex numbers. The eigenvalues of the matrices converge almost surely to the eigenvalues of the flow, which are distributed in law according to a sine-kernel point process. The eigenvectors of the matrices converge almost surely to vectors, which are distributed in law as Gaussian random fields on a countable set.
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Digital Object Identifier 10.1007/978-3-030-56409-4_8
Other Identification Number merlin-id:20937
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