Moments of Moments of the Characteristic Polynomials of Random Orthogonal and Symplectic Matrices

Claeys, Tom;Forkel, Johannes;Keating, Jonathan P.
(2022) Proceedings of the Royal society of London. Mathematics, physical sciences and engineering — Vol. 479, p. 20220652 (2023)

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  • Claeys, Tomorcid-logoUCLouvain
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  • Forkel, JohannesUniversity of Oxford
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  • Keating, Jonathan P.University of Oxford
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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 [14]. 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.
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Claeys, T., Forkel, J., & Keating, J. P. (2022). Moments of Moments of the Characteristic Polynomials of Random Orthogonal and Symplectic Matrices. Proceedings of the Royal society of London. Mathematics, physical sciences and engineering, 479, 20220652. https://doi.org/10.1098/rspa.2022.0652 (Original work published 2023)