{"paper":{"title":"On determinants identity minus Hankel matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Emilio Fedele, Martin Gebert","submitted_at":"2018-08-24T05:47:02Z","abstract_excerpt":"In this note, we study the asymptotics of the determinant $\\det(I_N - \\beta H_N)$ for $N$ large, where $H_N$ is the $N\\times N$ restriction of a Hankel matrix $H$ with finitely many jump discontinuities in its symbol satisfying $\\|H\\|\\leq 1$. Moreover, we assume $\\beta\\in\\mathbb C$ with $|\\beta|<1$ and $I_N$ denotes the identity matrix. We determine the first order asymtoptics as $N\\to\\infty$ of such determinants and show that they exhibit power-like asymptotic behaviour, with exponent depending on the height of the jumps. For example, for the $N \\times N$ truncation of the Hilbert matrix $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08009","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1808.08009/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}