{"paper":{"title":"On the moments of the moments of the characteristic polynomials of random unitary matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E. C. Bailey, J. P. Keating","submitted_at":"2018-07-17T18:01:01Z","abstract_excerpt":"Denoting by $P_N(A,\\theta)=\\det(I-Ae^{-i\\theta})$ the characteristic polynomial on the unit circle in the complex plane of an $N\\times N$ random unitary matrix $A$, we calculate the $k$th moment, defined with respect to an average over $A\\in U(N)$, of the random variable corresponding to the $2\\beta$th moment of $P_N(A,\\theta)$ with respect to the uniform measure $\\frac{d\\theta}{2\\pi}$, for all $k, \\beta\\in\\mathbb{N}$ . These moments of moments have played an important role in recent investigations of the extreme value statistics of characteristic polynomials and their connections with log-cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06605","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}