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

2019/10/28 by T. Assiotis, Theo Assiotis, Emma Bailey +6 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #math-ph #math.CO #math.MP #math.PR

paper · pdf · doi:10.48550/arxiv.1910.12576

31 pages, to appear in AIHPD

openalex publication_date 2019/10/28 · arxiv created 2022/11/30 · arxiv updated 2022/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

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• Asymptotics for averages over classical orthogonal ensembles
• A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants II

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