{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:TWCXBZXQUTDAHRSWS3X4PDNKCH","short_pith_number":"pith:TWCXBZXQ","schema_version":"1.0","canonical_sha256":"9d8570e6f0a4c603c65696efc78daa11e1982978c8d76a301e94c83b7dfb2164","source":{"kind":"arxiv","id":"1306.3082","version":3},"attestation_state":"computed","paper":{"title":"Conditioned random walks from Kac-Moody root systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.RT"],"primary_cat":"math.CO","authors_text":"C\\'edric Lecouvey (LMPT), Emmanuel Lesigne (LMPT), Marc Peign\\'e (LMPT)","submitted_at":"2013-06-13T11:22:30Z","abstract_excerpt":"Random paths are time continuous interpolations of random walks. By using Littelmann path model, we associate to each irreducible highest weight module of a Kac Moody algebra g a random path W. Under suitable hypotheses, we make explicit the probability of the event E: W never exits the Weyl chamber of g. We then give the law of the random walk defined by W conditioned by the event E and proves this law can be recovered by applying to W the generalized Pitmann transform introduced by Biane, Bougerol and O'Connell. This generalizes the main results of [10] and [16] to Kac Moody root systems and"},"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":"1306.3082","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-13T11:22:30Z","cross_cats_sorted":["math.PR","math.RT"],"title_canon_sha256":"2c3865db318179b7e9609cb274211cbf5cd3127bfc56d211bbf6839c28629416","abstract_canon_sha256":"055cd408205d0ec6704082e5c0c794f103227bb444a896495026763f10d44409"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:06.472648Z","signature_b64":"DY6RNf9DSdDLoHHt6sOMTy1fjX4WQ78NaY1aJvA2M+uDKK3sGaoSUsfrSvht4BP/8XkGyZsJylF0P0j0UBb4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d8570e6f0a4c603c65696efc78daa11e1982978c8d76a301e94c83b7dfb2164","last_reissued_at":"2026-05-18T03:04:06.472178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:06.472178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conditioned random walks from Kac-Moody root systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.RT"],"primary_cat":"math.CO","authors_text":"C\\'edric Lecouvey (LMPT), Emmanuel Lesigne (LMPT), Marc Peign\\'e (LMPT)","submitted_at":"2013-06-13T11:22:30Z","abstract_excerpt":"Random paths are time continuous interpolations of random walks. By using Littelmann path model, we associate to each irreducible highest weight module of a Kac Moody algebra g a random path W. Under suitable hypotheses, we make explicit the probability of the event E: W never exits the Weyl chamber of g. We then give the law of the random walk defined by W conditioned by the event E and proves this law can be recovered by applying to W the generalized Pitmann transform introduced by Biane, Bougerol and O'Connell. This generalizes the main results of [10] and [16] to Kac Moody root systems and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3082","kind":"arxiv","version":3},"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":"1306.3082","created_at":"2026-05-18T03:04:06.472250+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.3082v3","created_at":"2026-05-18T03:04:06.472250+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3082","created_at":"2026-05-18T03:04:06.472250+00:00"},{"alias_kind":"pith_short_12","alias_value":"TWCXBZXQUTDA","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"TWCXBZXQUTDAHRSW","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"TWCXBZXQ","created_at":"2026-05-18T12:28:02.375192+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/TWCXBZXQUTDAHRSWS3X4PDNKCH","json":"https://pith.science/pith/TWCXBZXQUTDAHRSWS3X4PDNKCH.json","graph_json":"https://pith.science/api/pith-number/TWCXBZXQUTDAHRSWS3X4PDNKCH/graph.json","events_json":"https://pith.science/api/pith-number/TWCXBZXQUTDAHRSWS3X4PDNKCH/events.json","paper":"https://pith.science/paper/TWCXBZXQ"},"agent_actions":{"view_html":"https://pith.science/pith/TWCXBZXQUTDAHRSWS3X4PDNKCH","download_json":"https://pith.science/pith/TWCXBZXQUTDAHRSWS3X4PDNKCH.json","view_paper":"https://pith.science/paper/TWCXBZXQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.3082&json=true","fetch_graph":"https://pith.science/api/pith-number/TWCXBZXQUTDAHRSWS3X4PDNKCH/graph.json","fetch_events":"https://pith.science/api/pith-number/TWCXBZXQUTDAHRSWS3X4PDNKCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TWCXBZXQUTDAHRSWS3X4PDNKCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TWCXBZXQUTDAHRSWS3X4PDNKCH/action/storage_attestation","attest_author":"https://pith.science/pith/TWCXBZXQUTDAHRSWS3X4PDNKCH/action/author_attestation","sign_citation":"https://pith.science/pith/TWCXBZXQUTDAHRSWS3X4PDNKCH/action/citation_signature","submit_replication":"https://pith.science/pith/TWCXBZXQUTDAHRSWS3X4PDNKCH/action/replication_record"}},"created_at":"2026-05-18T03:04:06.472250+00:00","updated_at":"2026-05-18T03:04:06.472250+00:00"}