{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:DMLC4ZXIPLH5DLY2YXLQX3LEVX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9ab1d015da51c6d1be8302605debce7c04b78d557163255c364d0c4af0bf5c0a","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-09-29T11:17:54Z","title_canon_sha256":"c9064b0b97c80af39e55b13f143afdd01774c44f13ac14c66a1b5bc4f711cd87"},"schema_version":"1.0","source":{"id":"2009.13928","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.13928","created_at":"2026-07-05T01:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"2009.13928v1","created_at":"2026-07-05T01:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.13928","created_at":"2026-07-05T01:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"DMLC4ZXIPLH5","created_at":"2026-07-05T01:38:46Z"},{"alias_kind":"pith_short_16","alias_value":"DMLC4ZXIPLH5DLY2","created_at":"2026-07-05T01:38:46Z"},{"alias_kind":"pith_short_8","alias_value":"DMLC4ZXI","created_at":"2026-07-05T01:38:46Z"}],"graph_snapshots":[{"event_id":"sha256:51a1e75769d08d8cb004643e044f797e0d1c5d8af38d73023532ef5a762d6c28","target":"graph","created_at":"2026-07-05T01:38:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.13928/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Jeannette H.C. Woerner, Michael Voit","cross_cats":["math-ph","math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-09-29T11:17:54Z","title":"Limit theorems for Bessel and Dunkl processes of large dimensions and free convolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.13928","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f3241b5fee43728dd22a2c89d3af19fd6fc4abb68f4fff47a612e8e2c6cd684a","target":"record","created_at":"2026-07-05T01:38:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9ab1d015da51c6d1be8302605debce7c04b78d557163255c364d0c4af0bf5c0a","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-09-29T11:17:54Z","title_canon_sha256":"c9064b0b97c80af39e55b13f143afdd01774c44f13ac14c66a1b5bc4f711cd87"},"schema_version":"1.0","source":{"id":"2009.13928","kind":"arxiv","version":1}},"canonical_sha256":"1b162e66e87acfd1af1ac5d70bed64adcacebdf671dbe7e4d6db0d7e2bd3b66a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b162e66e87acfd1af1ac5d70bed64adcacebdf671dbe7e4d6db0d7e2bd3b66a","first_computed_at":"2026-07-05T01:38:46.462391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:38:46.462391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ye7aMPtF7EtIH0Yinz1lVylpxTsKRs5PgW8lkW23IneIqEdNi8UYrBEQf5CmY12dvwNbF8Nen/i9B/ttw8QqDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:38:46.462802Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.13928","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3241b5fee43728dd22a2c89d3af19fd6fc4abb68f4fff47a612e8e2c6cd684a","sha256:51a1e75769d08d8cb004643e044f797e0d1c5d8af38d73023532ef5a762d6c28"],"state_sha256":"b6f43fa941365cba308e040fdfc3dbf159ddb6dca0b167a6b279ec6403456cb8"}