--- _id: '181' abstract: - lang: eng 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. acknowledgement: The work of the second author was also partially supported by the Hausdorff Center of Mathematics. article_processing_charge: No author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 - first_name: David T full_name: Renfrew, David T id: 4845BF6A-F248-11E8-B48F-1D18A9856A87 last_name: Renfrew orcid: 0000-0003-3493-121X citation: ama: Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290. doi:10.1137/17M1143125 apa: Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125 chicago: Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125. ieee: L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018. 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. mla: Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125. short: L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290. date_created: 2018-12-11T11:45:03Z date_published: 2018-01-01T00:00:00Z date_updated: 2023-09-15T12:05:52Z day: '01' department: - _id: LaEr doi: 10.1137/17M1143125 ec_funded: 1 external_id: arxiv: - '1708.01546' isi: - '000437018500032' intvolume: ' 50' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.01546 month: '01' oa: 1 oa_version: Published Version page: 3271 - 3290 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: 258F40A4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02080 name: Structured Non-Hermitian Random Matrices publication: SIAM Journal on Mathematical Analysis publication_status: published publisher: 'Society for Industrial and Applied Mathematics ' publist_id: '7740' quality_controlled: '1' scopus_import: '1' status: public title: Power law decay for systems of randomly coupled differential equations type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 50 year: '2018' ...