{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6235F42MV4WMVLUVX2UMTBFID7","short_pith_number":"pith:6235F42M","schema_version":"1.0","canonical_sha256":"f6b7d2f34caf2ccaae95bea8c984a81fd57b1f4dce6b596597816c7efa80286c","source":{"kind":"arxiv","id":"1908.11273","version":2},"attestation_state":"computed","paper":{"title":"The stochastic Airy operator at large temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Cyril Labb\\'e, Laure Dumaz","submitted_at":"2019-08-29T14:58:53Z","abstract_excerpt":"It was shown in [J. A. Ram\\'irez, B. Rider and B. Vir\\'ag. J. Amer. Math. Soc. 24, 919-944 (2011)] that the edge of the spectrum of $\\beta$ ensembles converges in the large $N$ limit to the bottom of the spectrum of the stochastic Airy operator. In the present paper, we obtain a complete description of the bottom of this spectrum when the temperature $1/\\beta$ goes to $\\infty$: we show that the point process of appropriately rescaled eigenvalues converges to a Poisson point process on $\\mathbb{R}$ of intensity $e^x dx$ and that the eigenfunctions converge to Dirac masses centered at IID points"},"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":"1908.11273","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-29T14:58:53Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"33816b37fecd08fbadeeffee34a26bc8008f94d82a295d8b4d86328c62360b38","abstract_canon_sha256":"322a2f9f10a75f8f4a9af48d5a469a6f3c99f5883fc47cf1b6e964d6bac483a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:33.323815Z","signature_b64":"3yLHPNSoOeO0T0Y1ne2gpG0qPn1qPIAIjpwrlYO3FnK6BKbd2pq4CHao2+Ogl4AZ1EC5EmKNet7W+8wzudnpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6b7d2f34caf2ccaae95bea8c984a81fd57b1f4dce6b596597816c7efa80286c","last_reissued_at":"2026-07-05T01:52:33.323411Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:33.323411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The stochastic Airy operator at large temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Cyril Labb\\'e, Laure Dumaz","submitted_at":"2019-08-29T14:58:53Z","abstract_excerpt":"It was shown in [J. A. Ram\\'irez, B. Rider and B. Vir\\'ag. J. Amer. Math. Soc. 24, 919-944 (2011)] that the edge of the spectrum of $\\beta$ ensembles converges in the large $N$ limit to the bottom of the spectrum of the stochastic Airy operator. In the present paper, we obtain a complete description of the bottom of this spectrum when the temperature $1/\\beta$ goes to $\\infty$: we show that the point process of appropriately rescaled eigenvalues converges to a Poisson point process on $\\mathbb{R}$ of intensity $e^x dx$ and that the eigenfunctions converge to Dirac masses centered at IID points"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.11273","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.11273/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.11273","created_at":"2026-07-05T01:52:33.323470+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.11273v2","created_at":"2026-07-05T01:52:33.323470+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.11273","created_at":"2026-07-05T01:52:33.323470+00:00"},{"alias_kind":"pith_short_12","alias_value":"6235F42MV4WM","created_at":"2026-07-05T01:52:33.323470+00:00"},{"alias_kind":"pith_short_16","alias_value":"6235F42MV4WMVLUV","created_at":"2026-07-05T01:52:33.323470+00:00"},{"alias_kind":"pith_short_8","alias_value":"6235F42M","created_at":"2026-07-05T01:52:33.323470+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6235F42MV4WMVLUVX2UMTBFID7","json":"https://pith.science/pith/6235F42MV4WMVLUVX2UMTBFID7.json","graph_json":"https://pith.science/api/pith-number/6235F42MV4WMVLUVX2UMTBFID7/graph.json","events_json":"https://pith.science/api/pith-number/6235F42MV4WMVLUVX2UMTBFID7/events.json","paper":"https://pith.science/paper/6235F42M"},"agent_actions":{"view_html":"https://pith.science/pith/6235F42MV4WMVLUVX2UMTBFID7","download_json":"https://pith.science/pith/6235F42MV4WMVLUVX2UMTBFID7.json","view_paper":"https://pith.science/paper/6235F42M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.11273&json=true","fetch_graph":"https://pith.science/api/pith-number/6235F42MV4WMVLUVX2UMTBFID7/graph.json","fetch_events":"https://pith.science/api/pith-number/6235F42MV4WMVLUVX2UMTBFID7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6235F42MV4WMVLUVX2UMTBFID7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6235F42MV4WMVLUVX2UMTBFID7/action/storage_attestation","attest_author":"https://pith.science/pith/6235F42MV4WMVLUVX2UMTBFID7/action/author_attestation","sign_citation":"https://pith.science/pith/6235F42MV4WMVLUVX2UMTBFID7/action/citation_signature","submit_replication":"https://pith.science/pith/6235F42MV4WMVLUVX2UMTBFID7/action/replication_record"}},"created_at":"2026-07-05T01:52:33.323470+00:00","updated_at":"2026-07-05T01:52:33.323470+00:00"}