{"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"}