{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LOPNZQNQUKK2BASKISXFSP5PU3","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":"4a499ae5070bacd4856e468b94f571356c70cb2ffaacfd139178650673c0c85e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-17T23:21:19Z","title_canon_sha256":"2e157f65da4258ad971979f12306c949a3e5056197bdaedc0b1665e27eb4b23e"},"schema_version":"1.0","source":{"id":"1003.3494","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3494","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3494v4","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3494","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"LOPNZQNQUKK2","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LOPNZQNQUKK2BASK","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LOPNZQNQ","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:1b389eb16f1e6d056f1dfa27770a61bbd9fd25ccd419f9d20ef71e83b5bbd842","target":"graph","created_at":"2026-05-18T04:14:38Z","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 random walks in a balanced random environment in $\\mathbb{Z}^d$, $d\\geq 2$. We first prove an invariance principle (for $d\\ge2$) and the transience of the random walks when $d\\ge 3$ (recurrence when $d=2$) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.","authors_text":"Ofer Zeitouni, Xiaoqin Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-17T23:21:19Z","title":"Quenched invariance principle for random walks in balanced random environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3494","kind":"arxiv","version":4},"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":"sha256:3e5317b7f92ffcf7dd6bbfdf8644f6c95363f6879a0146eba4dd3b7d1a92e0d3","target":"record","created_at":"2026-05-18T04:14:38Z","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":"4a499ae5070bacd4856e468b94f571356c70cb2ffaacfd139178650673c0c85e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-03-17T23:21:19Z","title_canon_sha256":"2e157f65da4258ad971979f12306c949a3e5056197bdaedc0b1665e27eb4b23e"},"schema_version":"1.0","source":{"id":"1003.3494","kind":"arxiv","version":4}},"canonical_sha256":"5b9edcc1b0a295a0824a44ae593fafa6ff9f3461be08c38e1b10a41615c01d2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b9edcc1b0a295a0824a44ae593fafa6ff9f3461be08c38e1b10a41615c01d2e","first_computed_at":"2026-05-18T04:14:38.253652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:38.253652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oM98tAv9Aa9mV/G3QR7ZISgwqOC3+a0fvoaBkEGZvU0gAwiFVuIw3jEQxOm1JD0R7gFrVYEQFHJlM3iN3k8XBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:38.254071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3494","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e5317b7f92ffcf7dd6bbfdf8644f6c95363f6879a0146eba4dd3b7d1a92e0d3","sha256:1b389eb16f1e6d056f1dfa27770a61bbd9fd25ccd419f9d20ef71e83b5bbd842"],"state_sha256":"4cacfdf713aafee2821425bd0a5df1461f9a6ac24d56cc09a612289c65800ff8"}