{"ddc":["510"],"date_created":"2024-07-21T22:01:01Z","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"LaEr"}],"year":"2024","publisher":"Oxford University Press","language":[{"iso":"eng"}],"file":[{"access_level":"open_access","creator":"dernst","file_size":1233508,"relation":"main_file","date_created":"2024-07-22T06:40:19Z","checksum":"f36a7dbf53f23d5833db711052e69b49","file_name":"2024_IMRN_Campbell.pdf","date_updated":"2024-07-22T06:40:19Z","success":1,"file_id":"17288","content_type":"application/pdf"}],"publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"abstract":[{"lang":"eng","text":"We extend the free convolution of Brown measures of R-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions."}],"oa":1,"citation":{"chicago":"Campbell, Andrew J, Sean O’Rourke, and David T Renfrew. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/imrn/rnae062\">https://doi.org/10.1093/imrn/rnae062</a>.","apa":"Campbell, A. J., O’Rourke, S., &#38; Renfrew, D. T. (2024). The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnae062\">https://doi.org/10.1093/imrn/rnae062</a>","ista":"Campbell AJ, O’Rourke S, Renfrew DT. 2024. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. 2024(13), 10189–10218.","ieee":"A. J. Campbell, S. O’Rourke, and D. T. Renfrew, “The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation,” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13. Oxford University Press, pp. 10189–10218, 2024.","short":"A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research Notices 2024 (2024) 10189–10218.","ama":"Campbell AJ, O’Rourke S, Renfrew DT. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. <i>International Mathematics Research Notices</i>. 2024;2024(13):10189-10218. doi:<a href=\"https://doi.org/10.1093/imrn/rnae062\">10.1093/imrn/rnae062</a>","mla":"Campbell, Andrew J., et al. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10189–218, doi:<a href=\"https://doi.org/10.1093/imrn/rnae062\">10.1093/imrn/rnae062</a>."},"publication_status":"published","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"corr_author":"1","article_type":"original","title":"The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation","date_updated":"2024-07-22T07:02:10Z","publication":"International Mathematics Research Notices","page":"10189-10218","scopus_import":"1","acknowledgement":"This work was supported by the National Science Foundation [Grant No. DMS-2143142 to S.O.]; and the European Research Council [Grant No. 101020331].The third author acknowledges the support of the University of Colorado Boulder, where a portion of this work was completed. The authors thank Martin Auer, Vadim Gorin, Brian Hall, and Noah Williams for comments, corrections, and references. The authors also wish to thank the anonymous referees for useful feedback and corrections.","intvolume":"      2024","doi":"10.1093/imrn/rnae062","quality_controlled":"1","date_published":"2024-07-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2024-07-22T06:40:19Z","day":"01","issue":"13","author":[{"full_name":"Campbell, Andrew J","last_name":"Campbell","first_name":"Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4"},{"last_name":"O'Rourke","first_name":"Sean","full_name":"O'Rourke, Sean"},{"full_name":"Renfrew, David T","orcid":"0000-0003-3493-121X","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","first_name":"David T","last_name":"Renfrew"}],"_id":"17281","volume":2024,"month":"07","oa_version":"Published Version","has_accepted_license":"1","status":"public","type":"journal_article"}