{"paper":{"title":"The Brown measure of a sum of two free nonselfadjoint random variables, one of which is R-diagonal","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.OA"],"primary_cat":"math.PR","authors_text":"Hari Bercovici, Ping Zhong","submitted_at":"2022-09-26T02:32:36Z","abstract_excerpt":"Suppose that $X_{1}$ and $X_{2}$ are two $*$-free (generally unbounded) random variables with Brown measures $\\mu_{X_{1}}$ and $\\mu_{X_{2}}$, respectively. Using properties of classical free additive convolutions, we develop a method for calculating $\\mu_{X_{1}+X_{2}}$when $X_{2}$ is $R$-diagonal. This method determines a density relative to Lebesgue measure on an open set whose closure contains the support of $\\mu_{X_{1}+X_{2}}$. Effective calculations are possible in important cases. Biane and Lehner were the first to make significant progress on the problem we consider, even in some cases i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.12379","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/2209.12379/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"}