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On the joint moments of the characteristic polynomials of random unitary matrices
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Assiotis, Theodoros, Keating, Jonathan P. and Warren, Jon (2022) On the joint moments of the characteristic polynomials of random unitary matrices. International Mathematics Research Notices, 2022 (18). pp. 14564-14603. doi:10.1093/imrn/rnab336 ISSN 1073-7928.
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Official URL: https://doi.org/10.1093/imrn/rnab336
Abstract
We establish the asymptotics of the joint moments of the characteristic polynomial of a random unitary matrix and its derivative for general real values of the exponents, proving a conjecture made by Hughes [ 40] in 2001. Moreover, we give a probabilistic representation for the leading order coefficient in the asymptotic in terms of a real-valued random variable that plays an important role in the ergodic decomposition of the Hua–Pickrell measures. This enables us to establish connections between the characteristic function of this random variable and the σ-Painlevé III’ equation.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
Library of Congress Subject Headings (LCSH): | Polynomials , Random polynomials , Random matrices, Ergodic theory | |||||||||
Journal or Publication Title: | International Mathematics Research Notices | |||||||||
Publisher: | Oxford University Press | |||||||||
ISSN: | 1073-7928 | |||||||||
Official Date: | September 2022 | |||||||||
Dates: |
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Volume: | 2022 | |||||||||
Number: | 18 | |||||||||
Page Range: | pp. 14564-14603 | |||||||||
DOI: | 10.1093/imrn/rnab336 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Theodoros Assiotis, Jonathan P Keating, Jon Warren, On the Joint Moments of the Characteristic Polynomials of Random Unitary Matrices, International Mathematics Research Notices, 2021;, rnab336, is available online at: https://doi.org/10.1093/imrn/rnab336 | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Copyright Holders: | © The Author(s) 2021. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com. | |||||||||
Date of first compliant deposit: | 6 January 2022 | |||||||||
Date of first compliant Open Access: | 14 December 2022 | |||||||||
RIOXX Funder/Project Grant: |
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Open Access Version: |
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