Tom Claeys, Johannes Forkel, Jonathan P. Keating
Published 2022-09-13Version 1
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.
Moments of the logarithmic derivative of characteristic polynomials from $SO(N)$ and $USp(2N)$
Asymptotics of mean-field $O(N)$ models
Asymptotics of eigenvalues of the Aharonov-Bohm operator with a strong $δ$-interaction on a loop
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