[{"oa_version":"Published Version","intvolume":" 50","status":"public","title":"Power law decay for systems of randomly coupled differential equations","_id":"181","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","issue":"3","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."}],"type":"journal_article","date_published":"2018-01-01T00:00:00Z","page":"3271 - 3290","citation":{"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.","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.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 3271–90, 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","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.","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"},"publication":"SIAM Journal on Mathematical Analysis","article_processing_charge":"No","day":"01","scopus_import":"1","volume":50,"date_updated":"2023-09-15T12:05:52Z","date_created":"2018-12-11T11:45:03Z","author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"},{"full_name":"Renfrew, David T","orcid":"0000-0003-3493-121X","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","last_name":"Renfrew","first_name":"David T"}],"publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2018","acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","publist_id":"7740","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1137/17M1143125","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"grant_number":"M02080","_id":"258F40A4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Structured Non-Hermitian Random Matrices"}],"isi":1,"quality_controlled":"1","external_id":{"arxiv":["1708.01546"],"isi":["000437018500032"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01546"}],"oa":1,"month":"01"},{"article_number":"1950009","ec_funded":1,"year":"2018","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"World Scientific Publishing","author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Mühlbacher, Peter","last_name":"Mühlbacher","first_name":"Peter"}],"date_updated":"2023-09-19T14:24:05Z","date_created":"2019-02-13T10:40:54Z","month":"09","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"main_file_link":[{"url":"https://arxiv.org/abs/1802.05175","open_access":"1"}],"oa":1,"external_id":{"arxiv":["1802.05175"],"isi":["000477677200002"]},"quality_controlled":"1","isi":1,"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"doi":"10.1142/s2010326319500096","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"lang":"eng","text":"We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices H=H∗ with centered independent entries and with a general matrix of variances Sxy=𝔼∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of the support of the self-consistent density of states. We establish a bound on this maximum in terms of norms of powers of S that substantially improves the earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727]. The key element of the proof is an effective Markov chain approximation for the contributions of the weighted Dyck paths appearing in the iterative solution of the corresponding Dyson equation."}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"5971","title":"Bounds on the norm of Wigner-type random matrices","status":"public","oa_version":"Preprint","scopus_import":"1","day":"26","article_processing_charge":"No","publication":"Random matrices: Theory and applications","citation":{"chicago":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications. World Scientific Publishing, 2018. https://doi.org/10.1142/s2010326319500096.","mla":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications, 1950009, World Scientific Publishing, 2018, doi:10.1142/s2010326319500096.","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","ista":"Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.","ieee":"L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications. World Scientific Publishing, 2018.","apa":"Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. Random Matrices: Theory and Applications. World Scientific Publishing. https://doi.org/10.1142/s2010326319500096","ama":"Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096"},"date_published":"2018-09-26T00:00:00Z"},{"ec_funded":1,"publist_id":"6383","year":"2018","publication_status":"published","publisher":"Oxford University Press","department":[{"_id":"LaEr"}],"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6179"}]},"date_updated":"2023-09-22T09:44:21Z","date_created":"2018-12-11T11:49:41Z","volume":2018,"month":"05","publication_identifier":{"issn":["10737928"]},"external_id":{"isi":["000441668300009"],"arxiv":["1608.05163"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.05163"}],"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"doi":"10.1093/imrn/rnw330","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"text":"We prove a new central limit theorem (CLT) for the difference of linear eigenvalue statistics of a Wigner random matrix H and its minor H and find that the fluctuation is much smaller than the fluctuations of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of H and H. In particular, our theorem identifies the fluctuation of Kerov's rectangular Young diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel measure follow the same limiting shape. For this, algebraically motivated, ensemble a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar to our result but the variance is different, indicating that the analogy between the two models has its limitations. Moreover, our theorem shows that Borodin's result [7] on the convergence of the spectral distribution of Wigner matrices to a Gaussian free field also holds in derivative sense.","lang":"eng"}],"issue":"10","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1012","status":"public","title":"Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues","intvolume":" 2018","oa_version":"Preprint","scopus_import":"1","day":"18","article_processing_charge":"No","publication":"International Mathematics Research Notices","citation":{"ista":"Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298.","apa":"Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnw330","ieee":"L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” International Mathematics Research Notices, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.","ama":"Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018;2018(10):3255-3298. doi:10.1093/imrn/rnw330","chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices. Oxford University Press, 2018. https://doi.org/10.1093/imrn/rnw330.","mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:10.1093/imrn/rnw330.","short":"L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018 (2018) 3255–3298."},"page":"3255-3298","date_published":"2018-05-18T00:00:00Z"},{"abstract":[{"text":"We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes.","lang":"eng"}],"issue":"2","type":"journal_article","file":[{"file_name":"2018_ALEA_Nejjar.pdf","access_level":"open_access","creator":"kschuh","file_size":394851,"content_type":"application/pdf","file_id":"5981","relation":"main_file","date_created":"2019-02-14T09:44:10Z","date_updated":"2020-07-14T12:47:46Z","checksum":"2ded46aa284a836a8cbb34133a64f1cb"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"70","title":"Transition to shocks in TASEP and decoupling of last passage times","ddc":["510"],"status":"public","intvolume":" 15","day":"01","has_accepted_license":"1","article_processing_charge":"No","scopus_import":"1","date_published":"2018-10-01T00:00:00Z","publication":"Latin American Journal of Probability and Mathematical Statistics","citation":{"chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49.","short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.","mla":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34, doi:10.30757/ALEA.v15-49.","ieee":"P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.","apa":"Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49","ista":"Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 15(2), 1311–1334.","ama":"Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334. doi:10.30757/ALEA.v15-49"},"article_type":"original","page":"1311-1334","file_date_updated":"2020-07-14T12:47:46Z","ec_funded":1,"author":[{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Nejjar","full_name":"Nejjar, Peter"}],"date_created":"2018-12-11T11:44:28Z","date_updated":"2023-10-10T13:11:29Z","volume":15,"year":"2018","publication_status":"published","publisher":"Instituto Nacional de Matematica Pura e Aplicada","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"month":"10","publication_identifier":{"issn":["1980-0436"]},"doi":"10.30757/ALEA.v15-49","language":[{"iso":"eng"}],"oa":1,"external_id":{"arxiv":["1705.08836"],"isi":["000460475800022"]},"isi":1,"quality_controlled":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"}]},{"date_published":"2018-06-04T00:00:00Z","publication":"Acta Scientiarum Mathematicarum","citation":{"short":"D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80.","mla":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2, Springer Nature, 2018, pp. 65–80, doi:10.14232/actasm-018-753-y.","chicago":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum. Springer Nature, 2018. https://doi.org/10.14232/actasm-018-753-y.","ama":"Virosztek D. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 2018;84(1-2):65-80. doi:10.14232/actasm-018-753-y","apa":"Virosztek, D. (2018). Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. Springer Nature. https://doi.org/10.14232/actasm-018-753-y","ieee":"D. Virosztek, “Maps on probability measures preserving certain distances - a survey and some new results,” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2. Springer Nature, pp. 65–80, 2018.","ista":"Virosztek D. 2018. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 84(1–2), 65–80."},"article_type":"original","page":"65 - 80","day":"04","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","_id":"284","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Maps on probability measures preserving certain distances - a survey and some new results","status":"public","intvolume":" 84","abstract":[{"lang":"eng","text":"Borel probability measures living on metric spaces are fundamental\r\nmathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are interested in the description of the structure of the isometries of such metric spaces. We overview some of the recent results of the topic and we also provide some new ones concerning the Wasserstein distance. More specifically, we consider the space of all Borel probability measures on the unit sphere of a Euclidean space endowed with the Wasserstein metric W_p for arbitrary p >= 1, and we show that the action of a Wasserstein isometry on the set of Dirac measures is induced by an isometry of the underlying unit sphere."}],"issue":"1-2","type":"journal_article","doi":"10.14232/actasm-018-753-y","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.03305"}],"external_id":{"arxiv":["1802.03305"]},"quality_controlled":"1","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"month":"06","publication_identifier":{"eissn":["2064-8316"],"issn":["0001-6969"]},"author":[{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511","first_name":"Daniel","last_name":"Virosztek","full_name":"Virosztek, Daniel"}],"date_updated":"2023-10-16T10:29:22Z","date_created":"2018-12-11T11:45:36Z","volume":84,"year":"2018","acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technol- ogy Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office, NKFIH (grant no. K124152).","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","publist_id":"7615","ec_funded":1}]