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We prove that P(\\Lambda > \\lambda) = e^{- (\\beta/2) \\lambda + 2 \\gamma \\lambda^{1/2}} \\lambda^{- (\\gamma(\\gamma+1))/(2\\beta) + \\gamma/4} E (\\beta, a) (1+o(1)) as \\lambda goes to infinity, in which \\gamma = (\\beta/2) (a+1)-1 and E(\\beta, a) is a constant (which we do not determine). This estimate complements/extends various results previously availabl"},"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":"1109.4121","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-19T18:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"d69319451e05b1ff87466225a2935575e980256d7f37607c5efc7b6e81e95860","abstract_canon_sha256":"21f35f6596121bd67704d69c64e3b407d29c2b4ad92913528f60ee2401891112"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:05.016595Z","signature_b64":"m00tq/l8MThn2Gad4SREnM6OEimDmpOqskijoV71tpRrQIxHnNcg64XjE/QHdRfpTWu7kqgGuoICSSQ8uJqfBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79325b89d84acb1bcb73215dd708364c32c54492340fbc64bfd8b9a7ff5a2a97","last_reissued_at":"2026-05-18T04:08:05.015953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:05.015953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hard edge tail asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Brian Rider, Jose A. 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