{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KOXCTGIYN4PBJ5C7N7ORGAMY2J","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cc9484a890294f197f8690e1b998500b6b506cae4d7c5d3983ba3daf48b21787","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-11T09:20:32Z","title_canon_sha256":"fa14900cf8d4d942eda68969ee86538418fd64b41f0c359be3828d7f67a7315b"},"schema_version":"1.0","source":{"id":"1807.04019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04019","created_at":"2026-05-18T00:10:58Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04019v1","created_at":"2026-05-18T00:10:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04019","created_at":"2026-05-18T00:10:58Z"},{"alias_kind":"pith_short_12","alias_value":"KOXCTGIYN4PB","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KOXCTGIYN4PBJ5C7","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KOXCTGIY","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:7ff0496a51d7f559ac4557f3850293615fe880eb7943fde2e4c8f556029b44af","target":"graph","created_at":"2026-05-18T00:10:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 ","authors_text":"Alexis Devulder (LMV), Fran\\c{c}oise Pene (LMBA), Nina Gantert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-11T09:20:32Z","title":"Collisions of several walkers in recurrent random environments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04019","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:09938688c463aa00038f6e1d4ec5c1979d23fdc4b9a46a4b1d0e5febdd1ed80f","target":"record","created_at":"2026-05-18T00:10:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cc9484a890294f197f8690e1b998500b6b506cae4d7c5d3983ba3daf48b21787","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-11T09:20:32Z","title_canon_sha256":"fa14900cf8d4d942eda68969ee86538418fd64b41f0c359be3828d7f67a7315b"},"schema_version":"1.0","source":{"id":"1807.04019","kind":"arxiv","version":1}},"canonical_sha256":"53ae2999186f1e14f45f6fdd130198d26e36c996081c2b2f0d3104a6b09f6653","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53ae2999186f1e14f45f6fdd130198d26e36c996081c2b2f0d3104a6b09f6653","first_computed_at":"2026-05-18T00:10:58.272397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:58.272397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/uAMQpz+9/a5tj544/5v+Uo7oumQKyga7srucTZgTWLhnZI9HO9sF159PtRv4y9bgq5mhQCqPtDHRVS28B5+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:58.273137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.04019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09938688c463aa00038f6e1d4ec5c1979d23fdc4b9a46a4b1d0e5febdd1ed80f","sha256:7ff0496a51d7f559ac4557f3850293615fe880eb7943fde2e4c8f556029b44af"],"state_sha256":"631e651e08f8b607d448409d713940fc5258b75be214dcf9c448ac0ac7208789"}