{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KOXCTGIYN4PBJ5C7N7ORGAMY2J","short_pith_number":"pith:KOXCTGIY","schema_version":"1.0","canonical_sha256":"53ae2999186f1e14f45f6fdd130198d26e36c996081c2b2f0d3104a6b09f6653","source":{"kind":"arxiv","id":"1807.04019","version":1},"attestation_state":"computed","paper":{"title":"Collisions of several walkers in recurrent random environments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexis Devulder (LMV), Fran\\c{c}oise Pene (LMBA), Nina Gantert","submitted_at":"2018-07-11T09:20:32Z","abstract_excerpt":"We consider d independent walkers on Z, m of them performing simple symmetric random walk and r = d -- m of them performing recurrent RWRE (Sinai walk), in I independent random environments. We show that the product is recurrent, almost surely, if and only if m $\\le$ 1 or m = d = 2. In the transient case with r $\\ge$ 1, we prove that the walkers meet infinitely often, almost surely, if and only if m = 2 and r $\\ge$ I = 1. In particular, while I does not have an influence for the recurrence or transience, it does play a role for the probability to have infinitely many meetings. To obtain these "},"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":"1807.04019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-11T09:20:32Z","cross_cats_sorted":[],"title_canon_sha256":"fa14900cf8d4d942eda68969ee86538418fd64b41f0c359be3828d7f67a7315b","abstract_canon_sha256":"cc9484a890294f197f8690e1b998500b6b506cae4d7c5d3983ba3daf48b21787"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:58.273137Z","signature_b64":"/uAMQpz+9/a5tj544/5v+Uo7oumQKyga7srucTZgTWLhnZI9HO9sF159PtRv4y9bgq5mhQCqPtDHRVS28B5+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53ae2999186f1e14f45f6fdd130198d26e36c996081c2b2f0d3104a6b09f6653","last_reissued_at":"2026-05-18T00:10:58.272397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:58.272397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Collisions of several walkers in recurrent random environments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexis Devulder (LMV), Fran\\c{c}oise Pene (LMBA), Nina Gantert","submitted_at":"2018-07-11T09:20:32Z","abstract_excerpt":"We consider d independent walkers on Z, m of them performing simple symmetric random walk and r = d -- m of them performing recurrent RWRE (Sinai walk), in I independent random environments. We show that the product is recurrent, almost surely, if and only if m $\\le$ 1 or m = d = 2. In the transient case with r $\\ge$ 1, we prove that the walkers meet infinitely often, almost surely, if and only if m = 2 and r $\\ge$ I = 1. In particular, while I does not have an influence for the recurrence or transience, it does play a role for the probability to have infinitely many meetings. To obtain these "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04019","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":"1807.04019","created_at":"2026-05-18T00:10:58.272537+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.04019v1","created_at":"2026-05-18T00:10:58.272537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04019","created_at":"2026-05-18T00:10:58.272537+00:00"},{"alias_kind":"pith_short_12","alias_value":"KOXCTGIYN4PB","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"KOXCTGIYN4PBJ5C7","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"KOXCTGIY","created_at":"2026-05-18T12:32:33.847187+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/KOXCTGIYN4PBJ5C7N7ORGAMY2J","json":"https://pith.science/pith/KOXCTGIYN4PBJ5C7N7ORGAMY2J.json","graph_json":"https://pith.science/api/pith-number/KOXCTGIYN4PBJ5C7N7ORGAMY2J/graph.json","events_json":"https://pith.science/api/pith-number/KOXCTGIYN4PBJ5C7N7ORGAMY2J/events.json","paper":"https://pith.science/paper/KOXCTGIY"},"agent_actions":{"view_html":"https://pith.science/pith/KOXCTGIYN4PBJ5C7N7ORGAMY2J","download_json":"https://pith.science/pith/KOXCTGIYN4PBJ5C7N7ORGAMY2J.json","view_paper":"https://pith.science/paper/KOXCTGIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.04019&json=true","fetch_graph":"https://pith.science/api/pith-number/KOXCTGIYN4PBJ5C7N7ORGAMY2J/graph.json","fetch_events":"https://pith.science/api/pith-number/KOXCTGIYN4PBJ5C7N7ORGAMY2J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KOXCTGIYN4PBJ5C7N7ORGAMY2J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KOXCTGIYN4PBJ5C7N7ORGAMY2J/action/storage_attestation","attest_author":"https://pith.science/pith/KOXCTGIYN4PBJ5C7N7ORGAMY2J/action/author_attestation","sign_citation":"https://pith.science/pith/KOXCTGIYN4PBJ5C7N7ORGAMY2J/action/citation_signature","submit_replication":"https://pith.science/pith/KOXCTGIYN4PBJ5C7N7ORGAMY2J/action/replication_record"}},"created_at":"2026-05-18T00:10:58.272537+00:00","updated_at":"2026-05-18T00:10:58.272537+00:00"}