{"paper":{"title":"Bi-Free Extreme Values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"Hao-Wei Huang, Jiun-Chau Wang","submitted_at":"2018-11-25T13:27:47Z","abstract_excerpt":"In this paper, we continue Voiculescu's recent work on the analogous extreme value theory in the context of bi-free probability theory. We derive various equivalent conditions for a bivariate distribution function to be bi-freely max-infinitely divisible. A bi-freely max-infinitely divisible distribution function can be expressed in terms of its marginals and a special form of copulas. Such a distribution function is shown to be also max-infinitely divisible in the classical sense. In addition, we characterize the set of bi-free extreme value distribution functions. A distribution function of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10007","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"}