{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HMJPAX5A35EPXRDRC4DAWPHT5H","short_pith_number":"pith:HMJPAX5A","schema_version":"1.0","canonical_sha256":"3b12f05fa0df48fbc47117060b3cf3e9e1dff1cb0caee7266dd99c64ec6ad9da","source":{"kind":"arxiv","id":"1310.6279","version":1},"attestation_state":"computed","paper":{"title":"Dirichlet random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gerard Letac, Mauro Piccioni","submitted_at":"2013-10-23T16:19:11Z","abstract_excerpt":"This article provides tools for the study of the Dirichlet random walk in $\\mathbb{R}^d$. By this we mean the random variable $W=X_1\\Theta_1+\\cdots+X_n\\Theta_n$ where $X=(X_1,\\ldots,X_n) \\sim \\mathcal{D}(q_1,\\ldots,q_n)$ is Dirichlet distributed and where $\\Theta_1,\\ldots \\Theta_n$ are iid, uniformly distributed on the unit sphere of $\\mathbb{R}^d$ and independent of $X.$ In particular we compute explicitely in a number of cases the distribution of $W.$ Some of our results appear already in the literature, in particular in the papers by G\\'erard Le Ca\\\"{e}r (2010, 2011). In these cases, our pr"},"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":"1310.6279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-23T16:19:11Z","cross_cats_sorted":[],"title_canon_sha256":"082284c13d4685ed1ada9827e26a8c8ee42808402320251ff5a1480c49948fc3","abstract_canon_sha256":"446609761a039aa1c3ef48b5ba11eee0d5101be045b7a48fb9191fe272e29ee2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:20.819473Z","signature_b64":"sTK96EnimqwtALv7V/RrzK0XlAJohHQhsJYECko2oeXM+TKfSThp3zs6uBMOQxwQxwCZzjOEYnyEI6X75XL4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b12f05fa0df48fbc47117060b3cf3e9e1dff1cb0caee7266dd99c64ec6ad9da","last_reissued_at":"2026-05-18T03:09:20.818563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:20.818563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dirichlet random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gerard Letac, Mauro Piccioni","submitted_at":"2013-10-23T16:19:11Z","abstract_excerpt":"This article provides tools for the study of the Dirichlet random walk in $\\mathbb{R}^d$. By this we mean the random variable $W=X_1\\Theta_1+\\cdots+X_n\\Theta_n$ where $X=(X_1,\\ldots,X_n) \\sim \\mathcal{D}(q_1,\\ldots,q_n)$ is Dirichlet distributed and where $\\Theta_1,\\ldots \\Theta_n$ are iid, uniformly distributed on the unit sphere of $\\mathbb{R}^d$ and independent of $X.$ In particular we compute explicitely in a number of cases the distribution of $W.$ Some of our results appear already in the literature, in particular in the papers by G\\'erard Le Ca\\\"{e}r (2010, 2011). In these cases, our pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6279","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":"1310.6279","created_at":"2026-05-18T03:09:20.818723+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.6279v1","created_at":"2026-05-18T03:09:20.818723+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6279","created_at":"2026-05-18T03:09:20.818723+00:00"},{"alias_kind":"pith_short_12","alias_value":"HMJPAX5A35EP","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HMJPAX5A35EPXRDR","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HMJPAX5A","created_at":"2026-05-18T12:27:46.883200+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/HMJPAX5A35EPXRDRC4DAWPHT5H","json":"https://pith.science/pith/HMJPAX5A35EPXRDRC4DAWPHT5H.json","graph_json":"https://pith.science/api/pith-number/HMJPAX5A35EPXRDRC4DAWPHT5H/graph.json","events_json":"https://pith.science/api/pith-number/HMJPAX5A35EPXRDRC4DAWPHT5H/events.json","paper":"https://pith.science/paper/HMJPAX5A"},"agent_actions":{"view_html":"https://pith.science/pith/HMJPAX5A35EPXRDRC4DAWPHT5H","download_json":"https://pith.science/pith/HMJPAX5A35EPXRDRC4DAWPHT5H.json","view_paper":"https://pith.science/paper/HMJPAX5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.6279&json=true","fetch_graph":"https://pith.science/api/pith-number/HMJPAX5A35EPXRDRC4DAWPHT5H/graph.json","fetch_events":"https://pith.science/api/pith-number/HMJPAX5A35EPXRDRC4DAWPHT5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HMJPAX5A35EPXRDRC4DAWPHT5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HMJPAX5A35EPXRDRC4DAWPHT5H/action/storage_attestation","attest_author":"https://pith.science/pith/HMJPAX5A35EPXRDRC4DAWPHT5H/action/author_attestation","sign_citation":"https://pith.science/pith/HMJPAX5A35EPXRDRC4DAWPHT5H/action/citation_signature","submit_replication":"https://pith.science/pith/HMJPAX5A35EPXRDRC4DAWPHT5H/action/replication_record"}},"created_at":"2026-05-18T03:09:20.818723+00:00","updated_at":"2026-05-18T03:09:20.818723+00:00"}