{"paper":{"title":"Weak local law and delocalization for the Sachdev-Ye-Kitaev model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Giorgio Cipolloni, Lucas Benigni","submitted_at":"2026-08-04T14:55:36Z","abstract_excerpt":"We establish a weak mesoscopic local law and quantitative eigenvector-delocalization estimates for the SYK Hamiltonian. For even $q\\ll N^{\\frac{1}{2}}$, we prove that the normalized Stieltjes transform converges uniformly on bounded energy intervals to that of the standard Gaussian law, down to scales of order $qN^{-\\frac{1}{2}}$, up to logarithmic factors. The result holds both on the full Hilbert space and in each fermion-parity sector. We derive mesoscopic eigenvalue counting and spectral form factor estimates, as well as an averaged inverse participation ratio bound. For fixed $q$, we furt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03771","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/2608.03771/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"}