{"paper":{"title":"On the support of the free additive convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OA","math.PR"],"primary_cat":"math-ph","authors_text":"Kevin Schnelli, Laszlo Erdos, Zhigang Bao","submitted_at":"2018-04-26T12:18:53Z","abstract_excerpt":"We consider the free additive convolution of two probability measures $\\mu$ and $\\nu$ on the real line and show that $\\mu\\boxplus\\nu$ is supported on a single interval if $\\mu$ and $\\nu$ each has single interval support. Moreover, the density of $\\mu\\boxplus\\nu$ is proven to vanish as a square root near the edges of its support if both $\\mu$ and $\\nu$ have power law behavior with exponents between $-1$ and $1$ near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [4]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11199","kind":"arxiv","version":3},"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"}