Abstract
By 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 (Fahs B. 2021 Communications in Mathematical Physics 383 , 685–730. (doi: 10.1007/s00220-021-03943-0 )). 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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