{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:45LD33JCRRUFJZMWF72SJQRH22","short_pith_number":"pith:45LD33JC","schema_version":"1.0","canonical_sha256":"e7563ded228c6854e5962ff524c227d6b6877051705462f8d8406622103c69c8","source":{"kind":"arxiv","id":"1601.06800","version":1},"attestation_state":"computed","paper":{"title":"Stochastic Airy semigroup through tridiagonal matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Mykhaylo Shkolnikov, Vadim Gorin","submitted_at":"2016-01-25T21:06:36Z","abstract_excerpt":"We determine the operator limit for large powers of random tridiagonal matrices as the size of the matrix grows. The result provides a novel expression in terms of functionals of Brownian motions for the Laplace transform of the Airy$_\\beta$ process, which describes the largest eigenvalues in the $\\beta$ ensembles of random matrix theory. Another consequence is a Feynman-Kac formula for the stochastic Airy operator of Ram\\'{i}rez, Rider, and Vir\\'{a}g. As a side result, we find that the difference between the area underneath a standard Brownian excursion and one half of the integral of its squ"},"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":"1601.06800","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-01-25T21:06:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3a645c6494ea604101d87a96b37755a12ef466d4f02229b1e761a1ccdb317946","abstract_canon_sha256":"d0b10f4454fd6733caf8dafadb117d8a03dee3c21f11a0312783a51b9c49fe4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:59.766240Z","signature_b64":"GU49RtwSwFdFJnYsuA6BxsYQjbyTcLDzOCg1GgsDWJPlmoh88PkaIe83Lrw13J+R5otBXzRZXxxKXc0+CMeuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7563ded228c6854e5962ff524c227d6b6877051705462f8d8406622103c69c8","last_reissued_at":"2026-05-18T01:21:59.765826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:59.765826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic Airy semigroup through tridiagonal matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Mykhaylo Shkolnikov, Vadim Gorin","submitted_at":"2016-01-25T21:06:36Z","abstract_excerpt":"We determine the operator limit for large powers of random tridiagonal matrices as the size of the matrix grows. The result provides a novel expression in terms of functionals of Brownian motions for the Laplace transform of the Airy$_\\beta$ process, which describes the largest eigenvalues in the $\\beta$ ensembles of random matrix theory. Another consequence is a Feynman-Kac formula for the stochastic Airy operator of Ram\\'{i}rez, Rider, and Vir\\'{a}g. As a side result, we find that the difference between the area underneath a standard Brownian excursion and one half of the integral of its squ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06800","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.06800","created_at":"2026-05-18T01:21:59.765883+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.06800v1","created_at":"2026-05-18T01:21:59.765883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06800","created_at":"2026-05-18T01:21:59.765883+00:00"},{"alias_kind":"pith_short_12","alias_value":"45LD33JCRRUF","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"45LD33JCRRUFJZMW","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"45LD33JC","created_at":"2026-05-18T12:29:58.707656+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/45LD33JCRRUFJZMWF72SJQRH22","json":"https://pith.science/pith/45LD33JCRRUFJZMWF72SJQRH22.json","graph_json":"https://pith.science/api/pith-number/45LD33JCRRUFJZMWF72SJQRH22/graph.json","events_json":"https://pith.science/api/pith-number/45LD33JCRRUFJZMWF72SJQRH22/events.json","paper":"https://pith.science/paper/45LD33JC"},"agent_actions":{"view_html":"https://pith.science/pith/45LD33JCRRUFJZMWF72SJQRH22","download_json":"https://pith.science/pith/45LD33JCRRUFJZMWF72SJQRH22.json","view_paper":"https://pith.science/paper/45LD33JC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.06800&json=true","fetch_graph":"https://pith.science/api/pith-number/45LD33JCRRUFJZMWF72SJQRH22/graph.json","fetch_events":"https://pith.science/api/pith-number/45LD33JCRRUFJZMWF72SJQRH22/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/45LD33JCRRUFJZMWF72SJQRH22/action/timestamp_anchor","attest_storage":"https://pith.science/pith/45LD33JCRRUFJZMWF72SJQRH22/action/storage_attestation","attest_author":"https://pith.science/pith/45LD33JCRRUFJZMWF72SJQRH22/action/author_attestation","sign_citation":"https://pith.science/pith/45LD33JCRRUFJZMWF72SJQRH22/action/citation_signature","submit_replication":"https://pith.science/pith/45LD33JCRRUFJZMWF72SJQRH22/action/replication_record"}},"created_at":"2026-05-18T01:21:59.765883+00:00","updated_at":"2026-05-18T01:21:59.765883+00:00"}