{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:57QCINWSI3QNZM2NJUNU3FFOUO","short_pith_number":"pith:57QCINWS","schema_version":"1.0","canonical_sha256":"efe02436d246e0dcb34d4d1b4d94aea3ba1b87d818fc22fa8d55f1b068c3301a","source":{"kind":"arxiv","id":"2403.18532","version":2},"attestation_state":"computed","paper":{"title":"Scaling limits for random walks on long range percolation clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Noam Berger, Yuki Tokushige","submitted_at":"2024-03-27T13:09:10Z","abstract_excerpt":"We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two vertices are connected behaves asymptotically as a negative power of distance between them. We prove that the scaling limit of simple random walk on the infinite component converges to an isotropic alpha-stable Levy process. This complements the work of Crawford and Sly, who proved the corresponding result for alpha between 0 and 1. The convergence holds in both the quenched and annealed senses."},"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":"2403.18532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-03-27T13:09:10Z","cross_cats_sorted":[],"title_canon_sha256":"51de14f623f595530d2591c25e96ee2f9aef0ca586530dd65f2061cc9104452a","abstract_canon_sha256":"72339d28bcd3efc96c6bc19cca0f2c38cc08e396e6cc46355388b867a69cd518"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:25:02.189183Z","signature_b64":"p0QDaxV8b0iaaAUuXl4rUS/zK8tUogGDWgQEhy0AT0QsncplZLG/f/3artOfwDwD0dRgqDzhH11oq/GJWRb6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efe02436d246e0dcb34d4d1b4d94aea3ba1b87d818fc22fa8d55f1b068c3301a","last_reissued_at":"2026-07-05T08:25:02.188683Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:25:02.188683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaling limits for random walks on long range percolation clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Noam Berger, Yuki Tokushige","submitted_at":"2024-03-27T13:09:10Z","abstract_excerpt":"We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two vertices are connected behaves asymptotically as a negative power of distance between them. We prove that the scaling limit of simple random walk on the infinite component converges to an isotropic alpha-stable Levy process. This complements the work of Crawford and Sly, who proved the corresponding result for alpha between 0 and 1. The convergence holds in both the quenched and annealed senses."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18532","kind":"arxiv","version":2},"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/2403.18532/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":"2403.18532","created_at":"2026-07-05T08:25:02.188744+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.18532v2","created_at":"2026-07-05T08:25:02.188744+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.18532","created_at":"2026-07-05T08:25:02.188744+00:00"},{"alias_kind":"pith_short_12","alias_value":"57QCINWSI3QN","created_at":"2026-07-05T08:25:02.188744+00:00"},{"alias_kind":"pith_short_16","alias_value":"57QCINWSI3QNZM2N","created_at":"2026-07-05T08:25:02.188744+00:00"},{"alias_kind":"pith_short_8","alias_value":"57QCINWS","created_at":"2026-07-05T08:25:02.188744+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.18808","citing_title":"Critical long-range percolation II: Low effective dimension","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/57QCINWSI3QNZM2NJUNU3FFOUO","json":"https://pith.science/pith/57QCINWSI3QNZM2NJUNU3FFOUO.json","graph_json":"https://pith.science/api/pith-number/57QCINWSI3QNZM2NJUNU3FFOUO/graph.json","events_json":"https://pith.science/api/pith-number/57QCINWSI3QNZM2NJUNU3FFOUO/events.json","paper":"https://pith.science/paper/57QCINWS"},"agent_actions":{"view_html":"https://pith.science/pith/57QCINWSI3QNZM2NJUNU3FFOUO","download_json":"https://pith.science/pith/57QCINWSI3QNZM2NJUNU3FFOUO.json","view_paper":"https://pith.science/paper/57QCINWS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.18532&json=true","fetch_graph":"https://pith.science/api/pith-number/57QCINWSI3QNZM2NJUNU3FFOUO/graph.json","fetch_events":"https://pith.science/api/pith-number/57QCINWSI3QNZM2NJUNU3FFOUO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/57QCINWSI3QNZM2NJUNU3FFOUO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/57QCINWSI3QNZM2NJUNU3FFOUO/action/storage_attestation","attest_author":"https://pith.science/pith/57QCINWSI3QNZM2NJUNU3FFOUO/action/author_attestation","sign_citation":"https://pith.science/pith/57QCINWSI3QNZM2NJUNU3FFOUO/action/citation_signature","submit_replication":"https://pith.science/pith/57QCINWSI3QNZM2NJUNU3FFOUO/action/replication_record"}},"created_at":"2026-07-05T08:25:02.188744+00:00","updated_at":"2026-07-05T08:25:02.188744+00:00"}