{"paper":{"title":"Range-Renewal Processes: SLLN, Power Law and Beyonds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Jiangang Ying, Jian-Sheng Xie, Xin-Xing Chen","submitted_at":"2013-05-08T14:29:29Z","abstract_excerpt":"Given $n$ samples of a regular discrete distribution $\\pi$, we prove in this article first a serial of SLLNs results (of Dvoretzky and Erd\\\"{o}s' type) which implies a typical power law when $\\pi$ is heavy-tailed. Constructing a (random) graph from the ordered $n$ samples, we can establish other laws for the degree-distribution of the graph. The phenomena of small world is also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1829","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"}