{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:26JU5CFJUQOUAIJKKNBHB2JALX","short_pith_number":"pith:26JU5CFJ","schema_version":"1.0","canonical_sha256":"d7934e88a9a41d40212a534270e9205df2b696a20b12deff7b28c7b78d6b760a","source":{"kind":"arxiv","id":"1204.5039","version":1},"attestation_state":"computed","paper":{"title":"Record Statistics for Multiple Random Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.PR","physics.data-an","q-fin.ST"],"primary_cat":"cond-mat.stat-mech","authors_text":"Gregor Wergen, Gregory Schehr, Satya N. Majumdar","submitted_at":"2012-04-23T12:16:33Z","abstract_excerpt":"We study the statistics of the number of records R_{n,N} for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We consider two cases: (I) when the variance \\sigma^2 of the jump distribution is finite and (II) when \\sigma^2 is divergent as in the case of L\\'evy flights with index 0 < \\mu < 2. In both cases we find that the mean record number <R_{n,N}> grows universally as \\sim \\alpha_N \\sqrt{n}"},"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":"1204.5039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-23T12:16:33Z","cross_cats_sorted":["cond-mat.dis-nn","math.PR","physics.data-an","q-fin.ST"],"title_canon_sha256":"d456511984186eefddf9281bc3a27dd4cad984b415c0b05af7e378b0fd766ea5","abstract_canon_sha256":"ac2b1079900568e125828fc75216a9726161aaf1e12bfe62fe16dd1ad354af41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:25.125597Z","signature_b64":"E0CEugwaKTfPQKEdPlVM7lEcSlHTDTjA4Bxj1n7RYbyOBKfMMlXG9b74acUYUO0fibQELIUgfQAtHP5OVzy2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7934e88a9a41d40212a534270e9205df2b696a20b12deff7b28c7b78d6b760a","last_reissued_at":"2026-05-18T03:50:25.124895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:25.124895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Record Statistics for Multiple Random Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.PR","physics.data-an","q-fin.ST"],"primary_cat":"cond-mat.stat-mech","authors_text":"Gregor Wergen, Gregory Schehr, Satya N. Majumdar","submitted_at":"2012-04-23T12:16:33Z","abstract_excerpt":"We study the statistics of the number of records R_{n,N} for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We consider two cases: (I) when the variance \\sigma^2 of the jump distribution is finite and (II) when \\sigma^2 is divergent as in the case of L\\'evy flights with index 0 < \\mu < 2. In both cases we find that the mean record number <R_{n,N}> grows universally as \\sim \\alpha_N \\sqrt{n}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5039","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":"1204.5039","created_at":"2026-05-18T03:50:25.124992+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.5039v1","created_at":"2026-05-18T03:50:25.124992+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5039","created_at":"2026-05-18T03:50:25.124992+00:00"},{"alias_kind":"pith_short_12","alias_value":"26JU5CFJUQOU","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"26JU5CFJUQOUAIJK","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"26JU5CFJ","created_at":"2026-05-18T12:26:50.516681+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/26JU5CFJUQOUAIJKKNBHB2JALX","json":"https://pith.science/pith/26JU5CFJUQOUAIJKKNBHB2JALX.json","graph_json":"https://pith.science/api/pith-number/26JU5CFJUQOUAIJKKNBHB2JALX/graph.json","events_json":"https://pith.science/api/pith-number/26JU5CFJUQOUAIJKKNBHB2JALX/events.json","paper":"https://pith.science/paper/26JU5CFJ"},"agent_actions":{"view_html":"https://pith.science/pith/26JU5CFJUQOUAIJKKNBHB2JALX","download_json":"https://pith.science/pith/26JU5CFJUQOUAIJKKNBHB2JALX.json","view_paper":"https://pith.science/paper/26JU5CFJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.5039&json=true","fetch_graph":"https://pith.science/api/pith-number/26JU5CFJUQOUAIJKKNBHB2JALX/graph.json","fetch_events":"https://pith.science/api/pith-number/26JU5CFJUQOUAIJKKNBHB2JALX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26JU5CFJUQOUAIJKKNBHB2JALX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26JU5CFJUQOUAIJKKNBHB2JALX/action/storage_attestation","attest_author":"https://pith.science/pith/26JU5CFJUQOUAIJKKNBHB2JALX/action/author_attestation","sign_citation":"https://pith.science/pith/26JU5CFJUQOUAIJKKNBHB2JALX/action/citation_signature","submit_replication":"https://pith.science/pith/26JU5CFJUQOUAIJKKNBHB2JALX/action/replication_record"}},"created_at":"2026-05-18T03:50:25.124992+00:00","updated_at":"2026-05-18T03:50:25.124992+00:00"}