{"paper":{"title":"Classical and free infinite divisibility for Boolean stable laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Octavio Arizmendi, Takahiro Hasebe","submitted_at":"2012-05-08T02:11:56Z","abstract_excerpt":"We completely determine the free infinite divisibility for the Boolean stable law which is parametrized by a stability index $\\alpha$ and an asymmetry coefficient $\\rho$. We prove that the Boolean stable law is freely infinitely divisible if and only if one of the following conditions holds: $0<\\alpha\\leq\\frac{1}{2}$; $\\frac{1}{2}<\\alpha\\leq\\frac{2}{3}$ and $2-\\frac{1}{\\alpha}\\leq\\rho \\leq \\frac{1}{\\alpha}-1$; $\\alpha=1,~\\rho=\\frac{1}{2}$. Positive Boolean stable laws corresponding to $\\rho =1$ and $\\alpha \\leq \\frac{1}{2}$ have completely monotonic densities and they are both freely and class"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1575","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"}