{"paper":{"title":"Approximation of projections of random vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Elizabeth Meckes","submitted_at":"2009-12-10T16:46:46Z","abstract_excerpt":"Let $X$ be a $d$-dimensional random vector and $X_\\theta$ its projection onto the span of a set of orthonormal vectors $\\{\\theta_1,...,\\theta_k\\}$. Conditions on the distribution of $X$ are given such that if $\\theta$ is chosen according to Haar measure on the Stiefel manifold, the bounded-Lipschitz distance from $X_\\theta$ to a Gaussian distribution is concentrated at its expectation; furthermore, an explicit bound is given for the expected distance, in terms of $d$, $k$, and the distribution of $X$, allowing consideration not just of fixed $k$ but of $k$ growing with $d$. The results are app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2044","kind":"arxiv","version":4},"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"}