{"paper":{"title":"Quenched large deviation principles for random projections of $\\ell_p^n$ balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Kavita Ramanan, Patrick Lopatto, Xiaoyu Xie","submitted_at":"2023-08-01T16:28:22Z","abstract_excerpt":"Let $(k_n)_{n \\in \\mathbb{N}}$ be a sequence of positive integers growing to infinity at a sublinear rate, $k_n \\rightarrow \\infty$ and $k_n/n \\rightarrow 0$ as $n \\rightarrow \\infty$. Given a sequence of $n$-dimensional random vectors $\\{Y^{(n)}\\}_{n \\in \\mathbb{N}}$ belonging to a certain class, which includes uniform distributions on suitably scaled $\\ell_p^n$-balls or $\\ell_p^n$-spheres, $p \\geq 2$, and product distributions with sub-Gaussian marginals, we study the large deviations behavior of the corresponding sequence of $k_n$-dimensional orthogonal projections $n^{-1/2} \\boldsymbol{a}_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.00649","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.00649/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"}