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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"},"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":"1201.3816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:09:45Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"7b55f8bb840f42f8bd5d9d9903b282c1d9f55b374395b35af7a7146eca578110","abstract_canon_sha256":"d5b5c128bddc344ada6ab2a3122adc45cd53c03aba5903b5c8001bd996d0dce7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:01.214243Z","signature_b64":"JbXnRR7cHU69po3LFciUXUluF/AmLfNdhYFFFHiUw021FzZDgZMcdEFpieCWwslOS43w4PSPGX5t3FHQqXtnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99ffe473ffbd90272d4b21d63954ae883e53bb27f31063512b1edbe9c83b5d00","last_reissued_at":"2026-05-18T03:52:01.213328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:01.213328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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