{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TTNL7KQ5ZHQYSP4GEXAFAWDUVB","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":"4fbed7cccca982af8fc39788fe8eb4a4ee1ac5a372cd85a051c9f21f05126500","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-13T16:05:28Z","title_canon_sha256":"f6e9c1cb0839ff4bc14589733a4f9390f82abccf66c01359b6593b8ed0fdd298"},"schema_version":"1.0","source":{"id":"1303.3199","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3199","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3199v3","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3199","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"TTNL7KQ5ZHQY","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TTNL7KQ5ZHQYSP4G","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TTNL7KQ5","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:6b10ef4b9018cec4f288dfba0fb03251b2099102e69c42e011bfb08a0da1c9ca","target":"graph","created_at":"2026-05-18T02:59:08Z","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":"In this paper we consider a null recurrent random walk in random environment on a super-critical Galton-Watson tree. We consider the case where the log-Laplace transform $\\psi$ of the branching process satisfies $\\psi(1)=\\psi'(1)=0$ for which G. Faraud, Y. Hu and Z. Shi in \\cite{HuShi10b} show that, with probability one, the largest generation visited by the walk, until the instant $n$, is of the order of $(\\log n)^3$. In \\cite{AndreolettiDebs1} we prove that the largest generation entirely visited behaves almost surely like $\\log n$ up to a constant. Here we study how the walk visits the gene","authors_text":"Pierre Andreoletti (MAPMO), Pierre Debs (MAPMO)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-13T16:05:28Z","title":"Spread of visited sites of a random walk along the generations of a branching process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3199","kind":"arxiv","version":3},"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:e0779953b6025808dafa656412ffce4a200db12fd70311ff37d16c739eb97504","target":"record","created_at":"2026-05-18T02:59:08Z","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":"4fbed7cccca982af8fc39788fe8eb4a4ee1ac5a372cd85a051c9f21f05126500","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-13T16:05:28Z","title_canon_sha256":"f6e9c1cb0839ff4bc14589733a4f9390f82abccf66c01359b6593b8ed0fdd298"},"schema_version":"1.0","source":{"id":"1303.3199","kind":"arxiv","version":3}},"canonical_sha256":"9cdabfaa1dc9e1893f8625c0505874a87037f44d6cb0ff189433bbe7e933f911","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cdabfaa1dc9e1893f8625c0505874a87037f44d6cb0ff189433bbe7e933f911","first_computed_at":"2026-05-18T02:59:08.792119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:08.792119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dLYh4Gx7crE7g6+jYyfNGziMMihqtfWBGrfCsE1MV0ezOsz1KtjHkzlqXtu1/Wi1AqZF/t+4InwBEWhvwgNMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:08.792664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3199","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0779953b6025808dafa656412ffce4a200db12fd70311ff37d16c739eb97504","sha256:6b10ef4b9018cec4f288dfba0fb03251b2099102e69c42e011bfb08a0da1c9ca"],"state_sha256":"45395b15a18f5a4f2c1308b21859872f6a6654638c16c3f5710397e461fe9a3c"}