{"paper":{"title":"Non-Conventional Limits of Random Sequences Related to Partitions of Integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"C. Vignat, J. Stoyanov","submitted_at":"2019-01-13T18:04:53Z","abstract_excerpt":"We deal with a sequence of integer-valued random variables $\\{Z_N\\}_{N=1}^{\\infty}$ which is related to restricted partitions of positive integers. We observe that $Z_N=X_1+ \\ldots + X_N$ for independent and bounded random variables $X_j$'s, so $Z_N$ has finite mean ${\\bf E}Z_N$ and variance ${\\bf Var}Z_N$. We want to find the limit distribution of ${\\hat Z}_N=\\left(Z_N-{\\bf E}Z_N\\right)/{\\sqrt{{\\bf Var}Z_N}}$ as $N \\to \\infty.$ While in many cases the limit distribution is normal, the main results established in this paper are that ${\\hat Z}_N \\overset{d}{\\to} Z_{*},$ where $Z_{*}$ is a bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04029","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"}