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 |
| Published: |
Royal Society
2023
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| Summary: | 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. |
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