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Entries are assumed to have Weibull distributions with tail decaying at rate $e^{-t^{\\alpha}}$ for $\\alpha >0$. While the law of large number results agree with the largest eigenvalue of sparse Hermitian matrices given in (Ganguly and Nam, '22) and (Ganguly, Hiesmayr and Nam, '22), large deviation results are surprisingly simpler, exhibiting a single transition at $\\alpha =2"},"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":"2406.09851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-06-14T09:01:25Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"26781e99ee2a618666069c5ff4ce9ef55287b50fd49f9d3e5d95b1659fd6d615","abstract_canon_sha256":"11c84b5bee9b2b9643c08b2fa324ea211d712ba6932ddae63a2151f434945007"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:32:43.024577Z","signature_b64":"Mmn3YybDSS3g4FalvhxTQydyJ97wIFuKItqhcPrXqWnINd7fNqTuu9lYKk9eE6Z0cU6O8Q5foMJDuZJBiVszDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3351986f83fc4ee19c7061372cdb39a0e4852f55c0a2c2c894b990e96830482b","last_reissued_at":"2026-07-05T08:32:43.024051Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:32:43.024051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large deviations for the largest singular value of sparse non-Hermitian matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Hyungwon Han","submitted_at":"2024-06-14T09:01:25Z","abstract_excerpt":"We prove a large deviation principle for the largest singular value of sparse non-Hermitian random matrices, or directed Erd\\H{o}s-R\\'enyi networks in the constant average degree regime $p =\\frac{d}{n}$ where $d$ is fixed. 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