{"paper":{"title":"Eigenvectors of Deformed Wigner Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Arash Amini, Farzan Haddadi","submitted_at":"2018-08-13T08:18:09Z","abstract_excerpt":"We investigate eigenvectors of rank-one deformations of random matrices $\\boldsymbol B = \\boldsymbol A + \\theta \\boldsymbol {uu}^*$ in which $\\boldsymbol A \\in \\mathbb R^{N \\times N}$ is a Wigner real symmetric random matrix, $\\theta \\in \\mathbb R^+$, and $\\boldsymbol u$ is uniformly distributed on the unit sphere. It is well known that for $\\theta > 1$ the eigenvector associated with the largest eigenvalue of $\\boldsymbol B$ closely estimates $\\boldsymbol u$ asymptotically, while for $\\theta < 1$ the eigenvectors of $\\boldsymbol B$ are uninformative about $\\boldsymbol u$. We examine $\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04098","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"}