{"paper":{"title":"Limit laws for random matrix products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"I2M), Jordan Emme (1), Pascal Hubert (2) ((1) FRUMAM","submitted_at":"2017-12-11T09:53:37Z","abstract_excerpt":"In this short note, we study the behaviour of a product of matrices with a simultaneous renormalization. Namely, for any sequence $(A\\_n)\\_{n\\in \\mathbb{N}}$ of $d\\times d$ complex matrices whose mean $A$ exists and whose norms' means are bounded, the product $\\left(I\\_d + \\frac1n A\\_0 \\right) \\dots \\left(I\\_d + \\frac1n A\\_{n-1} \\right) $ converges towards $\\exp{A}$. We give a dynamical version of this result as well as an illustration with an example of \"random walk\" on horocycles of the hyperbolic disc."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03698","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"}