{"paper":{"title":"On the strange domain of attraction to generalized Dickman distributions for sums of independent random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross G. Pinsky","submitted_at":"2016-11-22T09:13:38Z","abstract_excerpt":"Let $\\{B_k\\}_{k=1}^\\infty, \\{X_k\\}_{k=1}^\\infty$ all be independent random variables. Assume that $\\{B_k\\}_{k=1}^\\infty$ are $\\{0,1\\}$-valued Bernoulli random variables satisfying $B_k\\stackrel{\\text{dist}}{=}\\text{Ber}(p_k)$, with $\\sum_{k=1}^\\infty p_k=\\infty$, and assume that $\\{X_k\\}_{k=1}^\\infty$ satisfy:\n  $X_k>0,\\ \\ \\ \\mu_k\\equiv EX_k<\\infty, \\ \\ \\ \\lim_{k\\to\\infty}\\frac{X_k}{\\mu_k}\\stackrel{\\text{dist}}{=}1$. Let $M_n=\\sum_{k=1}^np_k\\mu_k$, assume that $M_n\\to\\infty$ and define the normalized sum of independent random variables $W_n=\\frac1{M_n}\\sum_{k=1}^nB_kX_k$. We give a general con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07207","kind":"arxiv","version":3},"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"}