{"paper":{"title":"Delocalization and Diffusion Profile for Random Band Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Antti Knowles, Horng-Tzer Yau, Jun Yin, Laszlo Erdos","submitted_at":"2012-05-25T11:49:50Z","abstract_excerpt":"We consider Hermitian and symmetric random band matrices $H = (h_{xy})$ in $d \\geq 1$ dimensions. The matrix entries $h_{xy}$, indexed by $x,y \\in (\\bZ/L\\bZ)^d$, are independent, centred random variables with variances $s_{xy} = \\E |h_{xy}|^2$. We assume that $s_{xy}$ is negligible if $|x-y|$ exceeds the band width $W$. In one dimension we prove that the eigenvectors of $H$ are delocalized if $W\\gg L^{4/5}$. We also show that the magnitude of the matrix entries $\\abs{G_{xy}}^2$ of the resolvent $G=G(z)=(H-z)^{-1}$ is self-averaging and we compute $\\E \\abs{G_{xy}}^2$. We show that, as $L\\to\\inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5669","kind":"arxiv","version":3},"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"}