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arXiv · 2209.06010

Moments of Moments of the Characteristic Polynomials of Random Orthogonal and Symplectic Matrices

Tom Claeys·Johannes Forkel·Jonathan P. Keating
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Abstract

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 way.

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Tom Claeys, Johannes Forkel, Jonathan P. Keating. 2022-09-13. Moments of Moments of the Characteristic Polynomials of Random Orthogonal and Symplectic Matrices. https://arxiv.org/abs/2209.06010

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