{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6UCIIYVD7AX4FDP7VAAVFAIGYG","short_pith_number":"pith:6UCIIYVD","schema_version":"1.0","canonical_sha256":"f5048462a3f82fc28dffa801528106c1a8b23e73c1b04d351f36983ec7b65b4f","source":{"kind":"arxiv","id":"1605.06958","version":1},"attestation_state":"computed","paper":{"title":"Convex Hulls of Multiple Random Walks: A Large-Deviation Study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexander K. Hartmann, Gunnar Claussen, Satya N. Majumdar, Timo Dewenter","submitted_at":"2016-05-23T09:49:09Z","abstract_excerpt":"We study the polygons governing the convex hull of a point set created by the steps of $n$ independent two-dimensional random walkers. Each such walk consists of $T$ discrete time steps, where $x$ and $y$ increments are i.i.d. Gaussian. We analyze area $A$ and perimeter $L$ of the convex hulls. We obtain probability densities for these two quantities over a large range of the support by using a large-deviation approach allowing us to study densities below $10^{-900}$. We find that the densities exhibit a universal scaling behavior as a function of $A/T$ and $L/\\sqrt{T}$, respectively. As in th"},"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":"1605.06958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-05-23T09:49:09Z","cross_cats_sorted":["physics.data-an"],"title_canon_sha256":"afe66d34b86754c62f02eeca5e0cd22435ffbde73e30afa5541b0b0dbd6ad08e","abstract_canon_sha256":"fea0626df5009ca8c8e6b0b31f78ec54de2a36af3f1af1238723a8b9c08569a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:12.564667Z","signature_b64":"2OceHtp/o9/F6im6kpZbNbyypFzSrOejTCRga7z+rubNjmow/wAmxo4wuRo6aBmw7g/vIQmnl1yxRX4krc6GDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5048462a3f82fc28dffa801528106c1a8b23e73c1b04d351f36983ec7b65b4f","last_reissued_at":"2026-05-18T00:57:12.564265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:12.564265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex Hulls of Multiple Random Walks: A Large-Deviation Study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexander K. Hartmann, Gunnar Claussen, Satya N. Majumdar, Timo Dewenter","submitted_at":"2016-05-23T09:49:09Z","abstract_excerpt":"We study the polygons governing the convex hull of a point set created by the steps of $n$ independent two-dimensional random walkers. Each such walk consists of $T$ discrete time steps, where $x$ and $y$ increments are i.i.d. Gaussian. We analyze area $A$ and perimeter $L$ of the convex hulls. We obtain probability densities for these two quantities over a large range of the support by using a large-deviation approach allowing us to study densities below $10^{-900}$. We find that the densities exhibit a universal scaling behavior as a function of $A/T$ and $L/\\sqrt{T}$, respectively. As in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06958","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":"1605.06958","created_at":"2026-05-18T00:57:12.564342+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.06958v1","created_at":"2026-05-18T00:57:12.564342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06958","created_at":"2026-05-18T00:57:12.564342+00:00"},{"alias_kind":"pith_short_12","alias_value":"6UCIIYVD7AX4","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"6UCIIYVD7AX4FDP7","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"6UCIIYVD","created_at":"2026-05-18T12:30:04.600751+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/6UCIIYVD7AX4FDP7VAAVFAIGYG","json":"https://pith.science/pith/6UCIIYVD7AX4FDP7VAAVFAIGYG.json","graph_json":"https://pith.science/api/pith-number/6UCIIYVD7AX4FDP7VAAVFAIGYG/graph.json","events_json":"https://pith.science/api/pith-number/6UCIIYVD7AX4FDP7VAAVFAIGYG/events.json","paper":"https://pith.science/paper/6UCIIYVD"},"agent_actions":{"view_html":"https://pith.science/pith/6UCIIYVD7AX4FDP7VAAVFAIGYG","download_json":"https://pith.science/pith/6UCIIYVD7AX4FDP7VAAVFAIGYG.json","view_paper":"https://pith.science/paper/6UCIIYVD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.06958&json=true","fetch_graph":"https://pith.science/api/pith-number/6UCIIYVD7AX4FDP7VAAVFAIGYG/graph.json","fetch_events":"https://pith.science/api/pith-number/6UCIIYVD7AX4FDP7VAAVFAIGYG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6UCIIYVD7AX4FDP7VAAVFAIGYG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6UCIIYVD7AX4FDP7VAAVFAIGYG/action/storage_attestation","attest_author":"https://pith.science/pith/6UCIIYVD7AX4FDP7VAAVFAIGYG/action/author_attestation","sign_citation":"https://pith.science/pith/6UCIIYVD7AX4FDP7VAAVFAIGYG/action/citation_signature","submit_replication":"https://pith.science/pith/6UCIIYVD7AX4FDP7VAAVFAIGYG/action/replication_record"}},"created_at":"2026-05-18T00:57:12.564342+00:00","updated_at":"2026-05-18T00:57:12.564342+00:00"}