{"paper":{"title":"General limit theorems for mixtures of free, monotone, and boolean independence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OA"],"primary_cat":"math.PR","authors_text":"David Jekel, Janusz Wysocza\\'nski, Lahcen Oussi","submitted_at":"2024-07-02T14:05:41Z","abstract_excerpt":"We study mixtures of free, monotone, and Boolean independence described by a directed graph $G = (V,E)$ in the context of $\\mathcal{T}$-free convolutions of Jekel and Liu. We prove general limit theorems for the associated additive convolution operations $\\boxplus_G$. For a sequence of digraphs $G_n = (V_n,E_n)$, we give sufficient conditions for the limit $\\widehat{\\mu} = \\lim_{n \\to \\infty} \\boxplus_{G_n}(\\mu_n)$ to exist whenever the Boolean convolution powers $\\mu_n^{\\uplus |V_n|}$ converge to some $\\mu$. This in particular includes central limit and Poisson limit theorems, as well as limi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02276","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.02276/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}