{"paper":{"title":"Concentration inequalities for random matrix products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amelia Henriksen, Rachel Ward","submitted_at":"2019-07-12T16:50:36Z","abstract_excerpt":"Suppose $\\{ X_k \\}_{k \\in \\mathbb{Z}}$ is a sequence of bounded independent random matrices with common dimension $d\\times d$ and common expectation $\\mathbb{E}[ X_k ]= X$. Under these general assumptions, the normalized random matrix product $$Z_n = (I + \\frac{1}{n}X_n)(I + \\frac{1}{n}X_{n-1}) \\cdots (I + \\frac{1}{n}X_1)$$ converges to $Z_n \\rightarrow e^{X}$ as $n \\rightarrow \\infty$. Normalized random matrix products of this form arise naturally in stochastic iterative algorithms, such as Oja's algorithm for streaming Principal Component Analysis. Here, we derive nonasymptotic concentration"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05833","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"}