{"paper":{"title":"Classical Scale Mixtures of Boolean Stable Laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Octavio Arizmend, Takahiro Hasebe","submitted_at":"2014-05-09T07:43:28Z","abstract_excerpt":"We study Boolean stable laws, $\\mathbf{b}_{\\alpha,\\rho}$, with stability index $\\alpha$ and asymmetry parameter $\\rho$. We show that the classical scale mixture of $\\mathbf{b}_{\\alpha,\\rho}$ coincides with a free mixture and also a monotone mixture of $\\mathbf{b}_{\\alpha,\\rho}$. For this purpose we define the multiplicative monotone convolution of probability measures, one is supported on the positive real line and the other is arbitrary.\n  We prove that any scale mixture of $\\mathbf{b}_{\\alpha,\\rho}$ is both classically and freely infinitely divisible for $\\alpha\\leq1/2$ and also for some $\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2162","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"}