{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SSRN3BHN7YVV6PNALMWVLAJK7S","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":"1386939cbd2c95d32b5216f3942885be721bdadd7ae060dc08fe043de5bb5b37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-28T11:22:40Z","title_canon_sha256":"f821235fc2020f0457eb9b7936310aaf49d9453bc434a287781a3e1e6b682b29"},"schema_version":"1.0","source":{"id":"1305.6448","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6448","created_at":"2026-05-18T00:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6448v5","created_at":"2026-05-18T00:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6448","created_at":"2026-05-18T00:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"SSRN3BHN7YVV","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SSRN3BHN7YVV6PNA","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SSRN3BHN","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:4952be72bc29720b56e258bfb6d2c1c2dbf1939d8c00c9636dbe0ccee8459f57","target":"graph","created_at":"2026-05-18T00:40:54Z","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":"Let $M_n$ be the minimal position at generation $n$, of a real-valued branching random walk in the boundary case. As $n \\to \\infty$, $M_n- {3 \\over 2} \\log n$ is tight (see [1][9][2]). We establish here a law of iterated logarithm for the upper limits of $M_n$: upon the system's non-extinction, $ \\limsup\\_{n\\to \\infty} {1\\over \\log \\log \\log n} ( M_n - {3\\over2} \\log n) = 1$ almost surely. We also study the problem of moderate deviations of $M_n$: $p(M_n- {3 \\over 2} \\log n > \\lambda)$ for $\\lambda\\to \\infty$ and $\\lambda=o(\\log n)$. This problem is closely related to the small deviations of a","authors_text":"Yueyun Hu (LAGA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-28T11:22:40Z","title":"How big is the minimum of a branching random walk?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6448","kind":"arxiv","version":5},"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":"sha256:1c3f670e358667e812daf00af19447a80e14d39d89c6d8458228fc164b923d76","target":"record","created_at":"2026-05-18T00:40:54Z","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":"1386939cbd2c95d32b5216f3942885be721bdadd7ae060dc08fe043de5bb5b37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-28T11:22:40Z","title_canon_sha256":"f821235fc2020f0457eb9b7936310aaf49d9453bc434a287781a3e1e6b682b29"},"schema_version":"1.0","source":{"id":"1305.6448","kind":"arxiv","version":5}},"canonical_sha256":"94a2dd84edfe2b5f3da05b2d55812afcbd555dafd51c7b5e35376c6932afcb77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94a2dd84edfe2b5f3da05b2d55812afcbd555dafd51c7b5e35376c6932afcb77","first_computed_at":"2026-05-18T00:40:54.259756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:54.259756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TROnLYds28wf4Abdn4UNhYI3WHIItQVZwHYOiMK/qha4Aoo+uG0+PfujTSY4GlJ4704AdFnHIDgSEMHs7S68Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:54.260195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6448","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c3f670e358667e812daf00af19447a80e14d39d89c6d8458228fc164b923d76","sha256:4952be72bc29720b56e258bfb6d2c1c2dbf1939d8c00c9636dbe0ccee8459f57"],"state_sha256":"1f87bf256bb58b98b52e49cb29f25c8953bfbf11a823ea2de9b277eede53130d"}