{"paper":{"title":"An Erd\\\" os-R\\' enyi law for nonconventional sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuri Kifer","submitted_at":"2015-10-08T08:44:03Z","abstract_excerpt":"We obtain rge Erd\\\" os-R\\' enyi type law of large numbers for \"nonconventional\" sums of the form $S_n=\\sum^n_{m=1}F(X_m,X_{2m},...,X_{\\ell m})$ where $X_1,X_2,...$ is a sequence of i.i.d. random variables and $F$ is a bounded Borel function. The proof relies on nonconventional large deviations obtained in [8]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02236","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"}