{"paper":{"title":"Delocalization of One-Dimensional Random Band Matrices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Horng-Tzer Yau, Jun Yin","submitted_at":"2025-01-03T09:23:18Z","abstract_excerpt":"Consider an $ N \\times N$ Hermitian one-dimensional random band matrix with band width $W > N^{1 / 2 + \\frak c} $ for any $ {\\frak c} > 0$. In the bulk of the spectrum and in the large $ N $ limit, we obtain the following results: (i) The semicircle law holds up to the scale $ N^{-1 + \\varepsilon} $ for any $ \\varepsilon > 0 $. (ii) All $ L^2 $- normalized eigenvectors are delocalized, meaning their $ L^\\infty$ norms are simultaneously bounded by $ N^{-\\frac{1}{2} + \\varepsilon} $ with overwhelming probability, for any $ \\varepsilon > 0 $. (iii) Quantum unique ergodicity holds in the sense tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01718","kind":"arxiv","version":4},"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/2501.01718/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"}