{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:4HEYZXEV3J2DN6JTHXQ5FY7ID7","short_pith_number":"pith:4HEYZXEV","schema_version":"1.0","canonical_sha256":"e1c98cdc95da7436f9333de1d2e3e81fde8e3bd6ff1216473112cba888c9ba02","source":{"kind":"arxiv","id":"1903.02972","version":1},"attestation_state":"computed","paper":{"title":"Random walks in a strongly sparse random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Iksanov, Alexander Marynych, Dariusz Buraczewski, Piotr Dyszewski","submitted_at":"2019-03-07T15:03:51Z","abstract_excerpt":"The integer points (sites) of the real line are marked by the positions of a standard random walk. We say that the set of marked sites is weakly, moderately or strongly sparse depending on whether the jumps of the standard random walk are supported by a bounded set, have finite or infinite mean, respectively. Focussing on the case of strong sparsity we consider a nearest neighbor random walk on the set of integers having jumps $\\pm 1$ with probability $1/2$ at every nonmarked site, whereas a random drift is imposed at every marked site. We prove new distributional limit theorems for the so def"},"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":"1903.02972","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-03-07T15:03:51Z","cross_cats_sorted":[],"title_canon_sha256":"3e0f4ee0da447e6195d281daca95ec30f67fb618d89b2b302c7b5e17f4d70ea9","abstract_canon_sha256":"e4f816671b3759060380fa871e0e92c14bd56eeefbbbbf6b7c8c04fd39312b89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:50.562949Z","signature_b64":"v9yOcvGakTQW2rNaKvWpHKGYcEgpxqx3zQl25G3JZwbjbldRm1FT4ndXz2YG+l1TKqJXzp6BDX4CZnR6wN8DBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1c98cdc95da7436f9333de1d2e3e81fde8e3bd6ff1216473112cba888c9ba02","last_reissued_at":"2026-05-17T23:51:50.562255Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:50.562255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random walks in a strongly sparse random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Iksanov, Alexander Marynych, Dariusz Buraczewski, Piotr Dyszewski","submitted_at":"2019-03-07T15:03:51Z","abstract_excerpt":"The integer points (sites) of the real line are marked by the positions of a standard random walk. We say that the set of marked sites is weakly, moderately or strongly sparse depending on whether the jumps of the standard random walk are supported by a bounded set, have finite or infinite mean, respectively. Focussing on the case of strong sparsity we consider a nearest neighbor random walk on the set of integers having jumps $\\pm 1$ with probability $1/2$ at every nonmarked site, whereas a random drift is imposed at every marked site. We prove new distributional limit theorems for the so def"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02972","kind":"arxiv","version":1},"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":"1903.02972","created_at":"2026-05-17T23:51:50.562347+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.02972v1","created_at":"2026-05-17T23:51:50.562347+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02972","created_at":"2026-05-17T23:51:50.562347+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HEYZXEV3J2D","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HEYZXEV3J2DN6JT","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HEYZXEV","created_at":"2026-05-18T12:33:10.108867+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/4HEYZXEV3J2DN6JTHXQ5FY7ID7","json":"https://pith.science/pith/4HEYZXEV3J2DN6JTHXQ5FY7ID7.json","graph_json":"https://pith.science/api/pith-number/4HEYZXEV3J2DN6JTHXQ5FY7ID7/graph.json","events_json":"https://pith.science/api/pith-number/4HEYZXEV3J2DN6JTHXQ5FY7ID7/events.json","paper":"https://pith.science/paper/4HEYZXEV"},"agent_actions":{"view_html":"https://pith.science/pith/4HEYZXEV3J2DN6JTHXQ5FY7ID7","download_json":"https://pith.science/pith/4HEYZXEV3J2DN6JTHXQ5FY7ID7.json","view_paper":"https://pith.science/paper/4HEYZXEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.02972&json=true","fetch_graph":"https://pith.science/api/pith-number/4HEYZXEV3J2DN6JTHXQ5FY7ID7/graph.json","fetch_events":"https://pith.science/api/pith-number/4HEYZXEV3J2DN6JTHXQ5FY7ID7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HEYZXEV3J2DN6JTHXQ5FY7ID7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HEYZXEV3J2DN6JTHXQ5FY7ID7/action/storage_attestation","attest_author":"https://pith.science/pith/4HEYZXEV3J2DN6JTHXQ5FY7ID7/action/author_attestation","sign_citation":"https://pith.science/pith/4HEYZXEV3J2DN6JTHXQ5FY7ID7/action/citation_signature","submit_replication":"https://pith.science/pith/4HEYZXEV3J2DN6JTHXQ5FY7ID7/action/replication_record"}},"created_at":"2026-05-17T23:51:50.562347+00:00","updated_at":"2026-05-17T23:51:50.562347+00:00"}