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Moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices

Abstract:
Using asymptotics of Toeplitz+Hankel determinants, we establish formulae for the asymptotics of the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices, as the matrix-size tends to infinity. Our results are analogous to those that Fahs obtained for random unitary matrices in [21]. A key feature of the formulae we derive is that the phase transitions in the moments of moments are seen to depend on the symmetry group in question in a significant way.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1098/rspa.2022.0652

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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:
Royal Society
Journal:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences More from this journal
Volume:
479
Article number:
20220652
Publication date:
2023-02-22
Acceptance date:
2023-01-19
DOI:
EISSN:
1471-2946
ISSN:
1364-5021
Language:
English
Keywords:
Pubs id:
1325008
Local pid:
pubs:1325008
Deposit date:
2023-01-24

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