{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:BRLAYCDKHOT76P4HZ3MNQQRD2M","short_pith_number":"pith:BRLAYCDK","schema_version":"1.0","canonical_sha256":"0c560c086a3ba7ff3f87ced8d84223d315ccddd82cfca498e9490feb1ca6bb4b","source":{"kind":"arxiv","id":"2402.05751","version":4},"attestation_state":"computed","paper":{"title":"Limit theorems for a strongly irreducible product of independent random matrices under optimal moment assumptions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Axel P\\'eneau","submitted_at":"2024-02-08T15:34:41Z","abstract_excerpt":"Let $\\nu$ be a probability distribution over the semi-group of square matrices of size $d \\ge 2$ over a locally compact field $\\mathbb{K}$, \\textit{e.g.} $\\mathbb{R}$.\n  We consider the random walk $\\overline{\\gamma}_n := \\gamma_0\\cdots\\gamma_{n-1}$ for $(\\gamma_k)_{k \\in \\mathbb{N}}$ independent of law $\\nu$.\n  Let $s_1 \\ge s_2 \\ge \\dots \\ge s_d$ be the singular values given by the Cartan projection.\n  Under a contraction assumption on $\\nu$, we show that $(\\log\\frac{s_1}{s_2}(\\overline{\\gamma}_n))_{n \\in\\mathbb{N}}$, escapes to infinity linearly and satisfies exponential large deviations ine"},"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":"2402.05751","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.PR","submitted_at":"2024-02-08T15:34:41Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3b727fee3b523fc0829b29b4d283b6f04cc7860fb04c0af2301ec217bcbadee6","abstract_canon_sha256":"7d713d7ed5616a1e0a68903bd0db239fa636498cf49a2105aa78b623cd4b11b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:25.124027Z","signature_b64":"NW4HA4MRBPLBc1mZ4ZM85XZT/uiNT7YkFYH7XFGt8NAQC7VbS0315G+Wq8RvmetfXpUrX4oj7dC+2oL96TmiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c560c086a3ba7ff3f87ced8d84223d315ccddd82cfca498e9490feb1ca6bb4b","last_reissued_at":"2026-05-20T00:05:25.123231Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:25.123231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit theorems for a strongly irreducible product of independent random matrices under optimal moment assumptions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Axel P\\'eneau","submitted_at":"2024-02-08T15:34:41Z","abstract_excerpt":"Let $\\nu$ be a probability distribution over the semi-group of square matrices of size $d \\ge 2$ over a locally compact field $\\mathbb{K}$, \\textit{e.g.} $\\mathbb{R}$.\n  We consider the random walk $\\overline{\\gamma}_n := \\gamma_0\\cdots\\gamma_{n-1}$ for $(\\gamma_k)_{k \\in \\mathbb{N}}$ independent of law $\\nu$.\n  Let $s_1 \\ge s_2 \\ge \\dots \\ge s_d$ be the singular values given by the Cartan projection.\n  Under a contraction assumption on $\\nu$, we show that $(\\log\\frac{s_1}{s_2}(\\overline{\\gamma}_n))_{n \\in\\mathbb{N}}$, escapes to infinity linearly and satisfies exponential large deviations ine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.05751","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.05751/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2402.05751","created_at":"2026-05-20T00:05:25.123365+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.05751v4","created_at":"2026-05-20T00:05:25.123365+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.05751","created_at":"2026-05-20T00:05:25.123365+00:00"},{"alias_kind":"pith_short_12","alias_value":"BRLAYCDKHOT7","created_at":"2026-05-20T00:05:25.123365+00:00"},{"alias_kind":"pith_short_16","alias_value":"BRLAYCDKHOT76P4H","created_at":"2026-05-20T00:05:25.123365+00:00"},{"alias_kind":"pith_short_8","alias_value":"BRLAYCDK","created_at":"2026-05-20T00:05:25.123365+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/BRLAYCDKHOT76P4HZ3MNQQRD2M","json":"https://pith.science/pith/BRLAYCDKHOT76P4HZ3MNQQRD2M.json","graph_json":"https://pith.science/api/pith-number/BRLAYCDKHOT76P4HZ3MNQQRD2M/graph.json","events_json":"https://pith.science/api/pith-number/BRLAYCDKHOT76P4HZ3MNQQRD2M/events.json","paper":"https://pith.science/paper/BRLAYCDK"},"agent_actions":{"view_html":"https://pith.science/pith/BRLAYCDKHOT76P4HZ3MNQQRD2M","download_json":"https://pith.science/pith/BRLAYCDKHOT76P4HZ3MNQQRD2M.json","view_paper":"https://pith.science/paper/BRLAYCDK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.05751&json=true","fetch_graph":"https://pith.science/api/pith-number/BRLAYCDKHOT76P4HZ3MNQQRD2M/graph.json","fetch_events":"https://pith.science/api/pith-number/BRLAYCDKHOT76P4HZ3MNQQRD2M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BRLAYCDKHOT76P4HZ3MNQQRD2M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BRLAYCDKHOT76P4HZ3MNQQRD2M/action/storage_attestation","attest_author":"https://pith.science/pith/BRLAYCDKHOT76P4HZ3MNQQRD2M/action/author_attestation","sign_citation":"https://pith.science/pith/BRLAYCDKHOT76P4HZ3MNQQRD2M/action/citation_signature","submit_replication":"https://pith.science/pith/BRLAYCDKHOT76P4HZ3MNQQRD2M/action/replication_record"}},"created_at":"2026-05-20T00:05:25.123365+00:00","updated_at":"2026-05-20T00:05:25.123365+00:00"}