{"paper":{"title":"On free infinite divisibility for classical Meixner distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Marek Bozejko, Takahiro Hasebe","submitted_at":"2013-02-20T12:25:58Z","abstract_excerpt":"We prove that symmetric Meixner distributions, whose probability densities are proportional to $|\\Gamma(t+ix)|^2$, are freely infinitely divisible for $0<t\\leq\\frac{1}{2}$. The case $t=\\frac{1}{2}$ corresponds to the law of L\\'evy's stochastic area whose probability density is $\\frac{1}{\\cosh(\\pi x)}$. A logistic distribution, whose probability density is proportional to $\\frac{1}{\\cosh^2(\\pi x)}$, is freely infinitely divisible too."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4885","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"}