{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DZFSKHXELCGBIXKUG4NN7NGH72","short_pith_number":"pith:DZFSKHXE","schema_version":"1.0","canonical_sha256":"1e4b251ee4588c145d54371adfb4c7fe851b7aeff190acc39206fd8e92924c17","source":{"kind":"arxiv","id":"1908.01385","version":1},"attestation_state":"computed","paper":{"title":"A Convergence Result for Dirichlet Semigroups on Tubular Neighbourhoods and the Marginals of Conditional Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Olaf Wittich, Vera Nobis","submitted_at":"2019-08-04T18:54:43Z","abstract_excerpt":"We investigate yet another approach to understand the limit behaviour of Brownian motion conditioned to stay within a tubular neighbourhood around a closed and connected submanifold of a Riemannian manifold. In this context, we identify a second order generator subject to Dirichlet conditions on the boundary of the tube and study its associated semigroups. After a suitable rescaling and renormalization procedure, we obtain convergence of these semigroups, both in $L^2$ and in Sobolev spaces of arbitrarily large index, to a limit semigroup, as the tube diameter tends to zero. As a byproduct, we"},"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":"1908.01385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-04T18:54:43Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d4fead70263cffeb8c88307d8f5031c9a4f60b113a4b35b5f833294e904fdc9d","abstract_canon_sha256":"dff5e8b7465f3ded46c99fc7d6e0c68af11c2ee6df14d6a6c34330e81ba29b99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:29.893774Z","signature_b64":"jn+0Z8szeD/6O8M5zrm90ZVSkz1ArL1WQCf1939Zw2ePW4de3yqpJ66n8Mkj6VPIWtoGjn1arVqlN0YQcbBZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e4b251ee4588c145d54371adfb4c7fe851b7aeff190acc39206fd8e92924c17","last_reissued_at":"2026-07-04T23:51:29.893442Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:29.893442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Convergence Result for Dirichlet Semigroups on Tubular Neighbourhoods and the Marginals of Conditional Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Olaf Wittich, Vera Nobis","submitted_at":"2019-08-04T18:54:43Z","abstract_excerpt":"We investigate yet another approach to understand the limit behaviour of Brownian motion conditioned to stay within a tubular neighbourhood around a closed and connected submanifold of a Riemannian manifold. In this context, we identify a second order generator subject to Dirichlet conditions on the boundary of the tube and study its associated semigroups. After a suitable rescaling and renormalization procedure, we obtain convergence of these semigroups, both in $L^2$ and in Sobolev spaces of arbitrarily large index, to a limit semigroup, as the tube diameter tends to zero. As a byproduct, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01385","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/1908.01385/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":"1908.01385","created_at":"2026-07-04T23:51:29.893497+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.01385v1","created_at":"2026-07-04T23:51:29.893497+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01385","created_at":"2026-07-04T23:51:29.893497+00:00"},{"alias_kind":"pith_short_12","alias_value":"DZFSKHXELCGB","created_at":"2026-07-04T23:51:29.893497+00:00"},{"alias_kind":"pith_short_16","alias_value":"DZFSKHXELCGBIXKU","created_at":"2026-07-04T23:51:29.893497+00:00"},{"alias_kind":"pith_short_8","alias_value":"DZFSKHXE","created_at":"2026-07-04T23:51:29.893497+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/DZFSKHXELCGBIXKUG4NN7NGH72","json":"https://pith.science/pith/DZFSKHXELCGBIXKUG4NN7NGH72.json","graph_json":"https://pith.science/api/pith-number/DZFSKHXELCGBIXKUG4NN7NGH72/graph.json","events_json":"https://pith.science/api/pith-number/DZFSKHXELCGBIXKUG4NN7NGH72/events.json","paper":"https://pith.science/paper/DZFSKHXE"},"agent_actions":{"view_html":"https://pith.science/pith/DZFSKHXELCGBIXKUG4NN7NGH72","download_json":"https://pith.science/pith/DZFSKHXELCGBIXKUG4NN7NGH72.json","view_paper":"https://pith.science/paper/DZFSKHXE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.01385&json=true","fetch_graph":"https://pith.science/api/pith-number/DZFSKHXELCGBIXKUG4NN7NGH72/graph.json","fetch_events":"https://pith.science/api/pith-number/DZFSKHXELCGBIXKUG4NN7NGH72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DZFSKHXELCGBIXKUG4NN7NGH72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DZFSKHXELCGBIXKUG4NN7NGH72/action/storage_attestation","attest_author":"https://pith.science/pith/DZFSKHXELCGBIXKUG4NN7NGH72/action/author_attestation","sign_citation":"https://pith.science/pith/DZFSKHXELCGBIXKUG4NN7NGH72/action/citation_signature","submit_replication":"https://pith.science/pith/DZFSKHXELCGBIXKUG4NN7NGH72/action/replication_record"}},"created_at":"2026-07-04T23:51:29.893497+00:00","updated_at":"2026-07-04T23:51:29.893497+00:00"}