On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices

Abstract

We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the matrix-size tends to infinity in terms of the volumes of certain regions involving continuous Gelfand-Tsetlin patterns with constraints. The results we find differ from those in the unitary case considered previously

31 pages, to appear in AIHPD

References in corpus (2)

• On the partition function of the Riemann zeta function, and the Fyodorov--Hiary--Keating conjecture
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Cited by in corpus (5)

• On the moments of the moments of $\zeta (1/2+it)$
• Asymptotics for averages over classical orthogonal ensembles
• On the critical-subcritical moments of moments of random characteristic polynomials: a GMC perspective
• Maxima of log-correlated fields: some recent developments
• On the moments of moments of random matrices and Ehrhart polynomials