{"paper":{"title":"A central limit theorem for scaled eigenvectors of random dot product graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Avanti Athreya, Carey E. Priebe, Daniel L. Sussman, David J. Marchette, Minh Tang, Vince Lyzinski","submitted_at":"2013-05-31T13:12:35Z","abstract_excerpt":"We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology outlined in \\citet{sussman2012universally} to construct consistent estimates for the latent positions, and we show that the appropriately scaled differences between the estimated and true latent positions converge to a mixture of Gaussian random variables. As a corollary, we obtain a central limit theorem for the first eigenvector of the adjacency matrix of an Er"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7388","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"}