{"paper":{"title":"Eigenvectors of non normal random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florent Benaych-Georges, Ofer Zeitouni","submitted_at":"2018-06-18T16:23:19Z","abstract_excerpt":"We study the angles between the eigenvectors of a random $n\\times n$ complex matrix $M$ with density $\\propto \\mathrm{e}^{-n\\operatorname{Tr}V(M^*M)}$ and $x\\mapsto V(x^2)$ convex. We prove that for unit eigenvectors $\\mathbf{v},\\mathbf{v}'$ associated with distinct eigenvalues $\\lambda,\\lambda'$ that are the closest to specified points $z,z'$ in the complex plane, the rescaled inner product $$\\sqrt{n}(\\lambda'-\\lambda)\\langle\\mathbf{v},\\mathbf{v}'\\rangle$$ is uniformly sub-Gaussian, and give a more precise statement in the case of the Ginibre ensemble."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06806","kind":"arxiv","version":2},"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"}