[{"isi":1,"intvolume":"      2024","file_date_updated":"2024-07-22T06:40:19Z","author":[{"id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","first_name":"Andrew J","full_name":"Campbell, Andrew J","last_name":"Campbell"},{"first_name":"Sean","last_name":"O'Rourke","full_name":"O'Rourke, Sean"},{"orcid":"0000-0003-3493-121X","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","first_name":"David T","last_name":"Renfrew","full_name":"Renfrew, David T"}],"publication":"International Mathematics Research Notices","scopus_import":"1","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"oa":1,"file":[{"access_level":"open_access","relation":"main_file","success":1,"checksum":"f36a7dbf53f23d5833db711052e69b49","content_type":"application/pdf","date_updated":"2024-07-22T06:40:19Z","file_name":"2024_IMRN_Campbell.pdf","creator":"dernst","date_created":"2024-07-22T06:40:19Z","file_id":"17288","file_size":1233508}],"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.","language":[{"iso":"eng"}],"corr_author":"1","department":[{"_id":"LaEr"}],"external_id":{"isi":["001198019500001"]},"date_created":"2024-07-21T22:01:01Z","publication_status":"published","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."}],"quality_controlled":"1","volume":2024,"page":"10189-10218","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2024","oa_version":"Published Version","date_updated":"2025-09-08T08:16:32Z","date_published":"2024-07-01T00:00:00Z","has_accepted_license":"1","publisher":"Oxford University Press","day":"01","type":"journal_article","issue":"13","tmp":{"short":"CC BY (4.0)","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)"},"status":"public","doi":"10.1093/imrn/rnae062","article_type":"original","ddc":["510"],"citation":{"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>","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>","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>.","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.","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>.","short":"A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research Notices 2024 (2024) 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."},"article_processing_charge":"Yes (via OA deal)","title":"The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation","month":"07","_id":"17281"},{"isi":1,"intvolume":"        50","ec_funded":1,"publication":"SIAM Journal on Mathematical Analysis","scopus_import":"1","author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"},{"orcid":"0000-0003-3493-121X","last_name":"Renfrew","full_name":"Renfrew, David T","first_name":"David T","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87"}],"oa":1,"acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","main_file_link":[{"url":"https://arxiv.org/abs/1708.01546","open_access":"1"}],"publication_status":"published","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:45:03Z","external_id":{"isi":["000437018500032"],"arxiv":["1708.01546"]},"department":[{"_id":"LaEr"}],"quality_controlled":"1","volume":50,"abstract":[{"text":"We consider large random matrices X with centered, independent entries but possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for f, g functions analytic on the spectrum of X. We use these results to compute the long time asymptotics for systems of coupled di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2.","lang":"eng"}],"date_updated":"2025-04-15T08:05:02Z","oa_version":"Published Version","year":"2018","date_published":"2018-01-01T00:00:00Z","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"call_identifier":"FWF","name":"Structured Non-Hermitian Random Matrices","_id":"258F40A4-B435-11E9-9278-68D0E5697425","grant_number":"M02080"}],"page":"3271 - 3290","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","issue":"3","day":"01","type":"journal_article","publisher":"Society for Industrial and Applied Mathematics ","arxiv":1,"doi":"10.1137/17M1143125","publist_id":"7740","month":"01","title":"Power law decay for systems of randomly coupled differential equations","_id":"181","citation":{"apa":"Erdös, L., Krüger, T. H., &#38; Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics . <a href=\"https://doi.org/10.1137/17M1143125\">https://doi.org/10.1137/17M1143125</a>","ama":"Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled differential equations. <i>SIAM Journal on Mathematical Analysis</i>. 2018;50(3):3271-3290. doi:<a href=\"https://doi.org/10.1137/17M1143125\">10.1137/17M1143125</a>","ista":"Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3), 3271–3290.","chicago":"Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics , 2018. <a href=\"https://doi.org/10.1137/17M1143125\">https://doi.org/10.1137/17M1143125</a>.","mla":"Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:<a href=\"https://doi.org/10.1137/17M1143125\">10.1137/17M1143125</a>.","short":"L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.","ieee":"L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018."},"article_processing_charge":"No"}]