{"oa":1,"oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_created":"2018-12-11T11:45:03Z","publisher":"Society for Industrial and Applied Mathematics ","scopus_import":"1","title":"Power law decay for systems of randomly coupled differential equations","quality_controlled":"1","status":"public","type":"journal_article","day":"01","month":"01","article_processing_charge":"No","date_updated":"2023-09-15T12:05:52Z","publication_status":"published","date_published":"2018-01-01T00:00:00Z","issue":"3","department":[{"_id":"LaEr"}],"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"}],"main_file_link":[{"url":"https://arxiv.org/abs/1708.01546","open_access":"1"}],"intvolume":"        50","volume":50,"publist_id":"7740","year":"2018","isi":1,"acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","project":[{"call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems"},{"call_identifier":"FWF","_id":"258F40A4-B435-11E9-9278-68D0E5697425","name":"Structured Non-Hermitian Random Matrices","grant_number":"M02080"}],"doi":"10.1137/17M1143125","page":"3271 - 3290","publication":"SIAM Journal on Mathematical Analysis","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603"},{"last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"},{"orcid":"0000-0003-3493-121X","last_name":"Renfrew","first_name":"David T","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","full_name":"Renfrew, David T"}],"external_id":{"arxiv":["1708.01546"],"isi":["000437018500032"]},"ec_funded":1,"citation":{"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>","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>","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>.","short":"L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.","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>.","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."},"language":[{"iso":"eng"}],"_id":"181"}