{"paper":{"title":"Free Bessel laws","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.PR","authors_text":"Benoit Collins, Mireille Capitaine, Serban Belinschi, Teodor Banica","submitted_at":"2007-10-31T19:10:06Z","abstract_excerpt":"We introduce and study a remarkable family of real probability measures $\\pi_{st}$, that we call free Bessel laws. These are related to the free Poisson law $\\pi$ via the formulae $\\pi_{s1}=\\pi^{\\boxtimes s}$ and $\\pi_{1t}=\\pi^{\\boxplus t}$. Our study includes: definition and basic properties, analytic aspects (supports, atoms, densities), combinatorial aspects (functional transforms, moments, partitions), and a discussion of the relation with random matrices and quantum groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5931","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"}