{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KH4OHLTBMP5Q2F3PGY4RFCUZDX","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":"64f6dcc1217df1a712a0553fa1c03eb2a4f2741a7684f7e95dfa3df3812476f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-03T15:30:21Z","title_canon_sha256":"c78418fc8bb7270420ab80a80dcd49284a39a4f7b8a77f1b7b89f8ccc033ed49"},"schema_version":"1.0","source":{"id":"1009.0700","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0700","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0700v1","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0700","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"KH4OHLTBMP5Q","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KH4OHLTBMP5Q2F3P","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KH4OHLTB","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:a49f11afba077f7a39b2b3c83eb1979e196be969279225998c691538236605ee","target":"graph","created_at":"2026-05-18T04:41:25Z","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 $\\{X_n\\}_{n\\in\\mathbb{N}}$ be a sequence of i.i.d. random variables in $\\mathbb{Z}^d$. Let $S_k=X_1+...+X_k$ and $Y_n(t)$ be the continuous process on $[0,1]$ for which $Y_n(k/n)=S_k/\\sqrt{n}$ $k=1,...,n$ and which is linearly interpolated elsewhere. The paper gives a generalization of results of Belkin, \\cite{B72} on the weak limit laws of $Y_n(t)$ conditioned to stay away from some small sets. In particular, it is shown that the diffusive limit of the random walk meander on $\\mathbb Z^d: d\\ge 2$ is the Brownian motion.","authors_text":"Domokos Sz\\'asz, Zsolt Pajor-Gyulai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-03T15:30:21Z","title":"Weak convergence of random walks conditioned to stay away"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0700","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":"sha256:9b4290e3698d6d0d78e7f649979a7abed193b08f2214e62bcb7ea4e4fc056d79","target":"record","created_at":"2026-05-18T04:41:25Z","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":"64f6dcc1217df1a712a0553fa1c03eb2a4f2741a7684f7e95dfa3df3812476f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-03T15:30:21Z","title_canon_sha256":"c78418fc8bb7270420ab80a80dcd49284a39a4f7b8a77f1b7b89f8ccc033ed49"},"schema_version":"1.0","source":{"id":"1009.0700","kind":"arxiv","version":1}},"canonical_sha256":"51f8e3ae6163fb0d176f3639128a991ddfa0700b12b7593a5b738dcade8adffe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51f8e3ae6163fb0d176f3639128a991ddfa0700b12b7593a5b738dcade8adffe","first_computed_at":"2026-05-18T04:41:25.605801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:25.605801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qESWTbYEGA9tdzMpJitLoXI8xNlewwssCtUuGe/SRAArJIGSLKFgI6UUXPvtVRqlBHgFrAWxqlOCaCOf/LjIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:25.606452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0700","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b4290e3698d6d0d78e7f649979a7abed193b08f2214e62bcb7ea4e4fc056d79","sha256:a49f11afba077f7a39b2b3c83eb1979e196be969279225998c691538236605ee"],"state_sha256":"f9a68180493649b09128e3ae6f6f4744e8e4421bd02e2680edbdebba97ab6ea3"}