{"paper":{"title":"Central Limit Theorems for Radial Random Walks on $p\\times q$ Matrices for $p\\to\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Michael Voit","submitted_at":"2012-01-18T15:09:45Z","abstract_excerpt":"Let $\\nu\\in M^1([0,\\infty[)$ be a fixed probability measure. For each dimension $p\\in\\b N$, let $(X_n^p)_{n\\ge1}$ be i.i.d. $\\b R^p$-valued radial random variables with radial distribution $\\nu$. We derive two central limit theorems for $ \\|X_1^p+...+X_n^p\\|_2$ for $n,p\\to\\infty$ with normal limits. The first CLT for $n>>p$ follows from known estimates of convergence in the CLT on $\\b R^p$, while the second CLT for $n<<p$ will be a consequence of asymptotic properties of Bessel convolutions. Both limit theorems are considered also for $U(p)$-invariant random walks on the space of $p\\times q$ m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3816","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"}