{"paper":{"title":"Random band matrices in the delocalized phase, I: Quantum unique ergodicity and universality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Horng-Tzer Yau, Jun Yin, Paul Bourgade","submitted_at":"2018-07-04T13:11:55Z","abstract_excerpt":"Consider $N\\times N$ symmetric one-dimensional random band matrices with general distribution of the entries and band width $W \\geq N^{3/4+\\varepsilon}$ for any $\\varepsilon>0$.\n  In the bulk of the spectrum and in the large $N$ limit, we obtain the following results.\n  (i) The semicircle law holds up to the scale $N^{-1+\\varepsilon}$ for any $\\varepsilon>0$.\n  (ii) The eigenvalues locally converge to the point process given by the Gaussian orthogonal ensemble at any fixed energy.\n  (iii) All eigenvectors are delocalized, meaning their ${\\rm L}^\\infty$ norms are all simultaneously bounded by $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01559","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":""},"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"}