{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:MMD4VUFBDXTNBWTLJOG4YVAUCS","short_pith_number":"pith:MMD4VUFB","schema_version":"1.0","canonical_sha256":"6307cad0a11de6d0da6b4b8dcc54141481c8c086e439a25e4004365592226755","source":{"kind":"arxiv","id":"1410.4832","version":2},"attestation_state":"computed","paper":{"title":"Hydrodynamic limit for a system of independent, sub-ballistic random walks in a common random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathon Peterson, Milton Jara","submitted_at":"2014-10-17T19:43:20Z","abstract_excerpt":"We consider a system of independent random walks in a common random environment. Previously, a hydrodynamic limit for the system of RWRE was proved under the assumption that the random walks were transient with positive speed. In this paper we instead consider the case where the random walks are transient but with a sublinear speed of the order $n^\\kappa$ for some $\\kappa \\in (0,1)$ and prove a quenched hydrodynamic limit for the system of random walks with time scaled by $n^{1/\\kappa}$ and space scaled by $n$. The most interesting feature of the hydrodynamic limit is that the influence of the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1410.4832","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-17T19:43:20Z","cross_cats_sorted":[],"title_canon_sha256":"0d43beff2865fd1178ec41f0869c861667230a064299c026761c243af0349c69","abstract_canon_sha256":"9c3898285a44b14d3f8d73d990c586aa7da371913d1908b5c31d984c9a1bbff8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:38.186819Z","signature_b64":"FCx92LwBlg0pzROroNaM4/7Fc8PLjY8XqeDNMjJqGIqsD7ZkzFcxpxChBa8b6Xu8lo8jGLPZNYCPkruFXMCaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6307cad0a11de6d0da6b4b8dcc54141481c8c086e439a25e4004365592226755","last_reissued_at":"2026-05-18T01:12:38.186468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:38.186468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hydrodynamic limit for a system of independent, sub-ballistic random walks in a common random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathon Peterson, Milton Jara","submitted_at":"2014-10-17T19:43:20Z","abstract_excerpt":"We consider a system of independent random walks in a common random environment. Previously, a hydrodynamic limit for the system of RWRE was proved under the assumption that the random walks were transient with positive speed. In this paper we instead consider the case where the random walks are transient but with a sublinear speed of the order $n^\\kappa$ for some $\\kappa \\in (0,1)$ and prove a quenched hydrodynamic limit for the system of random walks with time scaled by $n^{1/\\kappa}$ and space scaled by $n$. The most interesting feature of the hydrodynamic limit is that the influence of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4832","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.4832","created_at":"2026-05-18T01:12:38.186526+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.4832v2","created_at":"2026-05-18T01:12:38.186526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4832","created_at":"2026-05-18T01:12:38.186526+00:00"},{"alias_kind":"pith_short_12","alias_value":"MMD4VUFBDXTN","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"MMD4VUFBDXTNBWTL","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"MMD4VUFB","created_at":"2026-05-18T12:28:38.356838+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MMD4VUFBDXTNBWTLJOG4YVAUCS","json":"https://pith.science/pith/MMD4VUFBDXTNBWTLJOG4YVAUCS.json","graph_json":"https://pith.science/api/pith-number/MMD4VUFBDXTNBWTLJOG4YVAUCS/graph.json","events_json":"https://pith.science/api/pith-number/MMD4VUFBDXTNBWTLJOG4YVAUCS/events.json","paper":"https://pith.science/paper/MMD4VUFB"},"agent_actions":{"view_html":"https://pith.science/pith/MMD4VUFBDXTNBWTLJOG4YVAUCS","download_json":"https://pith.science/pith/MMD4VUFBDXTNBWTLJOG4YVAUCS.json","view_paper":"https://pith.science/paper/MMD4VUFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.4832&json=true","fetch_graph":"https://pith.science/api/pith-number/MMD4VUFBDXTNBWTLJOG4YVAUCS/graph.json","fetch_events":"https://pith.science/api/pith-number/MMD4VUFBDXTNBWTLJOG4YVAUCS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MMD4VUFBDXTNBWTLJOG4YVAUCS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MMD4VUFBDXTNBWTLJOG4YVAUCS/action/storage_attestation","attest_author":"https://pith.science/pith/MMD4VUFBDXTNBWTLJOG4YVAUCS/action/author_attestation","sign_citation":"https://pith.science/pith/MMD4VUFBDXTNBWTLJOG4YVAUCS/action/citation_signature","submit_replication":"https://pith.science/pith/MMD4VUFBDXTNBWTLJOG4YVAUCS/action/replication_record"}},"created_at":"2026-05-18T01:12:38.186526+00:00","updated_at":"2026-05-18T01:12:38.186526+00:00"}