{"paper":{"title":"Large deviations for high-dimensional 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":"Christoph Thaele, David Alonso-Guti\\'errez, Joscha Prochno","submitted_at":"2016-08-12T18:08:06Z","abstract_excerpt":"The paper provides a description of the large deviation behavior for the Euclidean norm of projections of $\\ell_p^n$-balls to high-dimensional random subspaces. More precisely, for each integer $n\\geq 1$, let $k_n\\in\\{1,\\ldots,n-1\\}$, $E^{(n)}$ be a uniform random $k_n$-dimensional subspace of $\\mathbb R^n$ and $X^{(n)}$ be a random point that is uniformly distributed in the $\\ell_p^n$-ball of $\\mathbb R^n$ for some $p\\in[1,\\infty]$. Then the Euclidean norms $\\|P_{E^{(n)}}X^{(n)}\\|_2$ of the orthogonal projections are shown to satisfy a large deviation principle as the space dimension $n$ tend"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03863","kind":"arxiv","version":3},"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"}