{"type":"journal_article","day":"01","article_processing_charge":"No","month":"11","date_updated":"2023-08-24T11:16:03Z","publication_status":"published","date_published":"2020-11-01T00:00:00Z","department":[{"_id":"LaEr"}],"abstract":[{"lang":"eng","text":"We consider the free additive convolution of two probability measures μ and ν on the real line and show that μ ⊞ v is supported on a single interval if μ and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven to vanish as a square root near the edges of its support if both μ and ν 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 [5]."}],"main_file_link":[{"url":"https://arxiv.org/abs/1804.11199","open_access":"1"}],"oa":1,"oa_version":"Preprint","date_created":"2021-02-07T23:01:15Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","scopus_import":"1","title":"On the support of the free additive convolution","quality_controlled":"1","status":"public","doi":"10.1007/s11854-020-0135-2","page":"323-348","author":[{"orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","first_name":"Zhigang"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","first_name":"László"},{"orcid":"0000-0003-0954-3231","last_name":"Schnelli","first_name":"Kevin","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"publication":"Journal d'Analyse Mathematique","external_id":{"arxiv":["1804.11199"],"isi":["000611879400008"]},"publication_identifier":{"eissn":["15658538"],"issn":["00217670"]},"ec_funded":1,"article_type":"original","citation":{"mla":"Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>, vol. 142, Springer Nature, 2020, pp. 323–48, doi:<a href=\"https://doi.org/10.1007/s11854-020-0135-2\">10.1007/s11854-020-0135-2</a>.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” <i>Journal d’Analyse Mathematique</i>, vol. 142. Springer Nature, pp. 323–348, 2020.","ama":"Bao Z, Erdös L, Schnelli K. On the support of the free additive convolution. <i>Journal d’Analyse Mathematique</i>. 2020;142:323-348. doi:<a href=\"https://doi.org/10.1007/s11854-020-0135-2\">10.1007/s11854-020-0135-2</a>","ista":"Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11854-020-0135-2\">https://doi.org/10.1007/s11854-020-0135-2</a>.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). On the support of the free additive convolution. <i>Journal d’Analyse Mathematique</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11854-020-0135-2\">https://doi.org/10.1007/s11854-020-0135-2</a>","short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348."},"language":[{"iso":"eng"}],"_id":"9104","intvolume":"       142","volume":142,"year":"2020","acknowledgement":"Supported in part by Hong Kong RGC Grant ECS 26301517.\r\nSupported in part by ERC Advanced Grant RANMAT No. 338804.\r\nSupported in part by the Knut and Alice Wallenberg Foundation and the Swedish Research Council Grant VR-2017-05195.","isi":1,"project":[{"call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems"}]}