{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EBEWIPQEB6WO2XBETXDY3RVUIH","short_pith_number":"pith:EBEWIPQE","schema_version":"1.0","canonical_sha256":"2049643e040faced5c249dc78dc6b441f377907d74f5d2b29400d2ed8b3b6b62","source":{"kind":"arxiv","id":"1805.10362","version":2},"attestation_state":"computed","paper":{"title":"Time-inhomogeneous random Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G.C.P. Innocentini, M. Novaes","submitted_at":"2018-05-25T21:04:18Z","abstract_excerpt":"We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\\cdots M_1$, with the factors $M_i$ drawn independently from an ensemble of random Markov matrices, whose columns are independent Dirichlet random variables. The statistical properties of the columns of $U(t)$, its largest eigenvalue and its spectrum are obtained exactly for $N=2$ and numerically investigated for general $N$. For large $t$, the columns are Dirichlet-distributed, however the distribution is differen"},"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":"1805.10362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-25T21:04:18Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b397aea8da76fb896481f36b8eb107298333148694fff26f5175371178d544ec","abstract_canon_sha256":"6a7b6c4ca2555f317f249efe7fb647fd4922a7853079efde5f8d96c2500d0975"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:55.599001Z","signature_b64":"qMfIdVH3ozlKxtPnD3ABMHZ25aH/bQZ6uWfZV1GAYbaWA2pTabKZV+NWWU7YGOKHY3Beca7o18GusHYNFbO0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2049643e040faced5c249dc78dc6b441f377907d74f5d2b29400d2ed8b3b6b62","last_reissued_at":"2026-05-18T00:00:55.598420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:55.598420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Time-inhomogeneous random Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G.C.P. Innocentini, M. Novaes","submitted_at":"2018-05-25T21:04:18Z","abstract_excerpt":"We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\\cdots M_1$, with the factors $M_i$ drawn independently from an ensemble of random Markov matrices, whose columns are independent Dirichlet random variables. The statistical properties of the columns of $U(t)$, its largest eigenvalue and its spectrum are obtained exactly for $N=2$ and numerically investigated for general $N$. For large $t$, the columns are Dirichlet-distributed, however the distribution is differen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10362","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":"1805.10362","created_at":"2026-05-18T00:00:55.598510+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.10362v2","created_at":"2026-05-18T00:00:55.598510+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10362","created_at":"2026-05-18T00:00:55.598510+00:00"},{"alias_kind":"pith_short_12","alias_value":"EBEWIPQEB6WO","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EBEWIPQEB6WO2XBE","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EBEWIPQE","created_at":"2026-05-18T12:32:22.470017+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/EBEWIPQEB6WO2XBETXDY3RVUIH","json":"https://pith.science/pith/EBEWIPQEB6WO2XBETXDY3RVUIH.json","graph_json":"https://pith.science/api/pith-number/EBEWIPQEB6WO2XBETXDY3RVUIH/graph.json","events_json":"https://pith.science/api/pith-number/EBEWIPQEB6WO2XBETXDY3RVUIH/events.json","paper":"https://pith.science/paper/EBEWIPQE"},"agent_actions":{"view_html":"https://pith.science/pith/EBEWIPQEB6WO2XBETXDY3RVUIH","download_json":"https://pith.science/pith/EBEWIPQEB6WO2XBETXDY3RVUIH.json","view_paper":"https://pith.science/paper/EBEWIPQE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.10362&json=true","fetch_graph":"https://pith.science/api/pith-number/EBEWIPQEB6WO2XBETXDY3RVUIH/graph.json","fetch_events":"https://pith.science/api/pith-number/EBEWIPQEB6WO2XBETXDY3RVUIH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EBEWIPQEB6WO2XBETXDY3RVUIH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EBEWIPQEB6WO2XBETXDY3RVUIH/action/storage_attestation","attest_author":"https://pith.science/pith/EBEWIPQEB6WO2XBETXDY3RVUIH/action/author_attestation","sign_citation":"https://pith.science/pith/EBEWIPQEB6WO2XBETXDY3RVUIH/action/citation_signature","submit_replication":"https://pith.science/pith/EBEWIPQEB6WO2XBETXDY3RVUIH/action/replication_record"}},"created_at":"2026-05-18T00:00:55.598510+00:00","updated_at":"2026-05-18T00:00:55.598510+00:00"}