{"paper":{"title":"Functional Erd\\\"os-R\\'enyi law of large numbers for nonconventional sums under weak dependence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yuri Kifer","submitted_at":"2016-08-05T12:18:11Z","abstract_excerpt":"We obtain a functional Erd\\H os-R\\' enyi law of large numbers for \"nonconventional\" sums of the form $\\Sig_n=\\sum_{m=1}^nF(X_m,X_{2m},...,X_{\\ell m})$ where $X_1,X_2,...$ is a sequence of exponentially fast $\\psi$-mixing random vectors and $F$ is a Borel vector function extendin in several directions our previous result concerning i.i.d. random variables $X_1,X_2,...$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01851","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":""},"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"}