{"paper":{"title":"Random band matrices in the delocalized phase, II: Generalized resolvent estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Fan Yang, Horng-Tzer Yau, Jun Yin, Paul Bourgade","submitted_at":"2018-07-04T13:20:20Z","abstract_excerpt":"This is the second part of a three part series abut delocalization for band matrices. In this paper, we consider a general class of $N\\times N$ random band matrices $H=(H_{ij})$ whose entries are centered random variables, independent up to a symmetry constraint. We assume that the variances $\\mathbb E |H_{ij}|^2$ form a band matrix with typical band width $1\\ll W\\ll N$. We consider the generalized resolvent of $H$ defined as $G(Z):=(H - Z)^{-1}$, where $Z$ is a deterministic diagonal matrix such that $Z_{ij}=\\left(z 1_{1\\leq i \\leq W}+\\widetilde z 1_{ i > W} \\right) \\delta_{ij}$, with two dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01562","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"}