On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices

Theo Assiotis; Emma C.  Bailey; J. P.  Keating

doi:10.4171/AIHPD/127

On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices

Theo Assiotis, Emma C. Bailey, J. P. Keating

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the matrix-size tends to infinity in terms of the volumes of certain regions involving continuous Gelfand-Tsetlin patterns with constraints. The results we find differ from those in the unitary case considered previously

Original language	English
Pages (from-to)	567-604
Number of pages	31
Journal	Annales de l’Institut Henri Poincaré D
Volume	9
Issue number	3
DOIs	https://doi.org/10.4171/AIHPD/127
Publication status	Published - 23 Dec 2022

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10.4171/AIHPD/127Licence: Creative Commons: Attribution (CC-BY)

1910.12576Accepted author manuscript, 336 KB

https://arxiv.org/abs/1910.12576

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title = "On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices",

abstract = "We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the matrix-size tends to infinity in terms of the volumes of certain regions involving continuous Gelfand-Tsetlin patterns with constraints. The results we find differ from those in the unitary case considered previously ",

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AU - Bailey, Emma C.

AU - Keating, J. P.

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AB - We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the matrix-size tends to infinity in terms of the volumes of certain regions involving continuous Gelfand-Tsetlin patterns with constraints. The results we find differ from those in the unitary case considered previously

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DO - 10.4171/AIHPD/127

M3 - Article

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JO - Annales de l’Institut Henri Poincaré D

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On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices

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