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Gaussian random variables with zero mean and covariance operator $\\Sigma={\\mathbb E}(X\\otimes X)$ taking values in a separable Hilbert space ${\\mathbb H}.$ Let $$ {\\bf r}(\\Sigma):=\\frac{{\\rm tr}(\\Sigma)}{\\|\\Sigma\\|_{\\infty}} $$ be the effective rank of $\\Sigma,$ ${\\rm tr}(\\Sigma)$ being the trace of $\\Sigma$ and $\\|\\Sigma\\|_{\\infty}$ being its operator norm. Let $$\\hat \\Sigma_n:=n^{-1}\\sum_{j=1}^n (X_j\\otimes X_j)$$ be the sample (empirical) covariance operator based on $(X_1,\\dots, X_n).$ The paper deals with a problem of estimation of spectral projectors of t"},"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":"1408.4643","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-08-20T13:20:50Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"50483b33640e7f8495359e296229af5c50c15f318715c04142577967bb883a54","abstract_canon_sha256":"aefea693050aeda0c4b5c42f0f18bca3babea79ed1f31eec3da8ae5e4d744f84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:40.225558Z","signature_b64":"sDT70S2EQ42XgXXMJ1dSoR4p/fyYhirYJScV7Nz8RMBqeS5xmkI/wREkcsutMvR+PTEgMvzvCczwyyW3/y+vDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b35ca47e8e319bf74132b26261a72131daf066eb6de3bee2c435c1d7d474d38","last_reissued_at":"2026-05-18T01:35:40.224776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:40.224776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics and Concentration Bounds for Bilinear Forms of Spectral Projectors of Sample Covariance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Karim Lounici, Vladimir Koltchinskii","submitted_at":"2014-08-20T13:20:50Z","abstract_excerpt":"Let $X,X_1,\\dots, X_n$ be i.i.d. 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