{"paper":{"title":"GOE Statistics for Levy Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Amol Aggarwal, Horng-Tzer Yau, Patrick Lopatto","submitted_at":"2018-06-19T17:46:27Z","abstract_excerpt":"In this paper we establish eigenvector delocalization and bulk universality for L\\'{e}vy matrices, which are real, symmetric, $N \\times N$ random matrices $\\textbf{H}$ whose upper triangular entries are independent, identically distributed $\\alpha$-stable laws. First, if $\\alpha \\in (1, 2)$ and $E \\in \\mathbb{R}$ is any energy bounded away from $0$, we show that every eigenvector of $\\textbf{H}$ corresponding to an eigenvalue near $E$ is completely delocalized and that the local spectral statistics of $\\textbf{H}$ around $E$ converge to those of the Gaussian Orthogonal Ensemble (GOE) as $N$ te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07363","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1806.07363/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"}