{"paper":{"title":"Cram\\'er's theorem is atypical","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kavita Ramanan, Nina Gantert, Steven Soojin Kim","submitted_at":"2015-08-18T18:19:18Z","abstract_excerpt":"The empirical mean of $n$ independent and identically distributed (i.i.d.) random variables $(X_1,\\dots,X_n)$ can be viewed as a suitably normalized scalar projection of the $n$-dimensional random vector $X^{(n)}\\doteq(X_1,\\dots,X_n)$ in the direction of the unit vector $n^{-1/2}(1,1,\\dots,1) \\in \\mathbb{S}^{n-1}$. The large deviation principle (LDP) for such projections as $n\\rightarrow\\infty$ is given by the classical Cram\\'er's theorem. We prove an LDP for the sequence of normalized scalar projections of $X^{(n)}$ in the direction of a generic unit vector $\\theta^{(n)} \\in \\mathbb{S}^{n-1}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04402","kind":"arxiv","version":2},"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"}