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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.04098","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-13T08:18:09Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"838e89604cbc76dd94cb8b676155d1765fcb30817c72e7edf5f96caf2feb4d36","abstract_canon_sha256":"d63db5997595be03d57ef0d6a0661747a26ccfc24f11ede3327cb33ae727512b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:18.885929Z","signature_b64":"MTtDtzMniXh5wSFzsE0UCzEgFxzRaZuvs64K476Op1zHCQpV4r8nGNWmkliZQ6HOWVBbucVdSLon/psWgQeAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dd594ad6223415723155b53150648fc017fe462d58815e65d1b3ee189225772","last_reissued_at":"2026-05-18T00:08:18.885466Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:18.885466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\boldsymbol u$. 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