{"paper":{"title":"A Khintchine Decomposition for Free Probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"John D. Williams","submitted_at":"2010-09-24T22:12:06Z","abstract_excerpt":"Let $\\mu$ be a probability measure on the real line. In this paper we prove that there exists a decomposition $\\mu = \\mu_{0} \\boxplus \\mu_{1} \\boxplus \\... \\boxplus \\mu_{n} \\boxplus \\...$ such that $\\mu_{0}$ is infinitely divisible and $\\mu_{i}$ is indecomposable for $i \\geq 1$. Additionally, we prove that the family of all $\\boxplus$-divisors of a measure $\\mu$ is compact up to translation. Analogous results are also proven in the case of multiplicative convolution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4955","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"}