Journal article
On the joint moments of the characteristic polynomials of random unitary matrices
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Access Document
- Files:
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(Preview, Accepted manuscript, pdf, 265.4KB, Terms of use)
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- Publisher copy:
- 10.1093/imrn/rnab336
Authors
- Publisher:
- Oxford University Press
- Journal:
- International Mathematics Research Notices More from this journal
- Volume:
- 2022
- Issue:
- 18
- Pages:
- 14564–14603
- Publication date:
- 2021-12-14
- Acceptance date:
- 2021-11-05
- DOI:
- EISSN:
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1687-0247
- ISSN:
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1073-7928
- Language:
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English
- Keywords:
- Pubs id:
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1207463
- Local pid:
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pubs:1207463
- Deposit date:
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2021-11-05
Terms of use
- Copyright holder:
- Assiotis et al.
- Copyright date:
- 2021
- Rights statement:
- © The Author(s) 2021. Published by Oxford University Press. All rights reserved.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Oxford University Press at: https://doi.org/10.1093/imrn/rnab336
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