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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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Publisher copy:
10.1093/imrn/rnab336

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Queen's College
Role:
Author
ORCID:
0000-0003-0864-038X


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:
1687-0247
ISSN:
1073-7928


Language:
English
Keywords:
Pubs id:
1207463
Local pid:
pubs:1207463
Deposit date:
2021-11-05

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