{"paper":{"title":"Limit theorems for the least common multiple of a random set of integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.PR","authors_text":"Alexander Marynych, Gerold Alsmeyer, Zakhar Kabluchko","submitted_at":"2018-01-26T18:56:13Z","abstract_excerpt":"Let $L_{n}$ be the least common multiple of a random set of integers obtained from $\\{1,\\ldots,n\\}$ by retaining each element with probability $\\theta\\in (0,1)$ independently of the others. We prove that the process $(\\log L_{\\lfloor nt\\rfloor})_{t\\in [0,1]}$, after centering and normalization, converges weakly to a certain Gaussian process that is not Brownian motion. Further results include a strong law of large numbers for $\\log L_{n}$ as well as Poisson limit theorems in regimes when $\\theta$ depends on $n$ in an appropriate way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08934","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"}