{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:DMLC4ZXIPLH5DLY2YXLQX3LEVX","short_pith_number":"pith:DMLC4ZXI","schema_version":"1.0","canonical_sha256":"1b162e66e87acfd1af1ac5d70bed64adcacebdf671dbe7e4d6db0d7e2bd3b66a","source":{"kind":"arxiv","id":"2009.13928","version":1},"attestation_state":"computed","paper":{"title":"Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Jeannette H.C. Woerner, Michael Voit","submitted_at":"2020-09-29T11:17:54Z","abstract_excerpt":"We study Bessel and Dunkl processes $(X_{t,k})_{t\\ge0}$ on $\\mathbb R^N$ with possibly multivariate coupling constants $k\\ge0$. These processes describe interacting particle systems of Calogero-Moser-Sutherland type with $N$ particles. For the root systems $A_{N-1}$ and $B_N$ these Bessel processes are related with $\\beta$-Hermite and $\\beta$-Laguerre ensembles. Moreover, for the frozen case $k=\\infty$, these processes degenerate to deterministic or pure jump processes. We use the generators for Bessel and Dunkl processes of types A and B and derive analogues of Wigner's semicircle and Marchen"},"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":"2009.13928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-09-29T11:17:54Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"c9064b0b97c80af39e55b13f143afdd01774c44f13ac14c66a1b5bc4f711cd87","abstract_canon_sha256":"9ab1d015da51c6d1be8302605debce7c04b78d557163255c364d0c4af0bf5c0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:38:46.462802Z","signature_b64":"ye7aMPtF7EtIH0Yinz1lVylpxTsKRs5PgW8lkW23IneIqEdNi8UYrBEQf5CmY12dvwNbF8Nen/i9B/ttw8QqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b162e66e87acfd1af1ac5d70bed64adcacebdf671dbe7e4d6db0d7e2bd3b66a","last_reissued_at":"2026-07-05T01:38:46.462391Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:38:46.462391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Jeannette H.C. Woerner, Michael Voit","submitted_at":"2020-09-29T11:17:54Z","abstract_excerpt":"We study Bessel and Dunkl processes $(X_{t,k})_{t\\ge0}$ on $\\mathbb R^N$ with possibly multivariate coupling constants $k\\ge0$. These processes describe interacting particle systems of Calogero-Moser-Sutherland type with $N$ particles. For the root systems $A_{N-1}$ and $B_N$ these Bessel processes are related with $\\beta$-Hermite and $\\beta$-Laguerre ensembles. Moreover, for the frozen case $k=\\infty$, these processes degenerate to deterministic or pure jump processes. We use the generators for Bessel and Dunkl processes of types A and B and derive analogues of Wigner's semicircle and Marchen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.13928","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.13928/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":"2009.13928","created_at":"2026-07-05T01:38:46.462448+00:00"},{"alias_kind":"arxiv_version","alias_value":"2009.13928v1","created_at":"2026-07-05T01:38:46.462448+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.13928","created_at":"2026-07-05T01:38:46.462448+00:00"},{"alias_kind":"pith_short_12","alias_value":"DMLC4ZXIPLH5","created_at":"2026-07-05T01:38:46.462448+00:00"},{"alias_kind":"pith_short_16","alias_value":"DMLC4ZXIPLH5DLY2","created_at":"2026-07-05T01:38:46.462448+00:00"},{"alias_kind":"pith_short_8","alias_value":"DMLC4ZXI","created_at":"2026-07-05T01:38:46.462448+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.06859","citing_title":"The Rectangular Finite Free Heat Flow","ref_index":51,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DMLC4ZXIPLH5DLY2YXLQX3LEVX","json":"https://pith.science/pith/DMLC4ZXIPLH5DLY2YXLQX3LEVX.json","graph_json":"https://pith.science/api/pith-number/DMLC4ZXIPLH5DLY2YXLQX3LEVX/graph.json","events_json":"https://pith.science/api/pith-number/DMLC4ZXIPLH5DLY2YXLQX3LEVX/events.json","paper":"https://pith.science/paper/DMLC4ZXI"},"agent_actions":{"view_html":"https://pith.science/pith/DMLC4ZXIPLH5DLY2YXLQX3LEVX","download_json":"https://pith.science/pith/DMLC4ZXIPLH5DLY2YXLQX3LEVX.json","view_paper":"https://pith.science/paper/DMLC4ZXI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2009.13928&json=true","fetch_graph":"https://pith.science/api/pith-number/DMLC4ZXIPLH5DLY2YXLQX3LEVX/graph.json","fetch_events":"https://pith.science/api/pith-number/DMLC4ZXIPLH5DLY2YXLQX3LEVX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DMLC4ZXIPLH5DLY2YXLQX3LEVX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DMLC4ZXIPLH5DLY2YXLQX3LEVX/action/storage_attestation","attest_author":"https://pith.science/pith/DMLC4ZXIPLH5DLY2YXLQX3LEVX/action/author_attestation","sign_citation":"https://pith.science/pith/DMLC4ZXIPLH5DLY2YXLQX3LEVX/action/citation_signature","submit_replication":"https://pith.science/pith/DMLC4ZXIPLH5DLY2YXLQX3LEVX/action/replication_record"}},"created_at":"2026-07-05T01:38:46.462448+00:00","updated_at":"2026-07-05T01:38:46.462448+00:00"}