Moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices
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 r...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Royal Society
2023
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| _version_ | 1826309588032421888 |
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| author | Claeys, T Forkel, J Keating, JP |
| author_facet | Claeys, T Forkel, J Keating, JP |
| author_sort | Claeys, T |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T07:37:59Z |
| format | Journal article |
| id | oxford-uuid:70d4f5f2-3253-4393-853d-30f9b0700ac1 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:37:59Z |
| publishDate | 2023 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:70d4f5f2-3253-4393-853d-30f9b0700ac12023-03-24T09:27:43ZMoments of moments of the characteristic polynomials of random orthogonal and symplectic matricesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:70d4f5f2-3253-4393-853d-30f9b0700ac1EnglishSymplectic ElementsRoyal Society2023Claeys, TForkel, JKeating, JPUsing 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. |
| spellingShingle | Claeys, T Forkel, J Keating, JP Moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices |
| title | Moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices |
| title_full | Moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices |
| title_fullStr | Moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices |
| title_full_unstemmed | Moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices |
| title_short | Moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices |
| title_sort | moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices |
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