--- _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' ... --- _id: '5971' 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=\U0001D53C∣∣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." article_number: '1950009' 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: Peter full_name: Mühlbacher, Peter last_name: Mühlbacher citation: ama: 'Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096' 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' 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.' ieee: 'L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications. World Scientific Publishing, 2018.' ista: 'Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.' 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).' date_created: 2019-02-13T10:40:54Z date_published: 2018-09-26T00:00:00Z date_updated: 2023-09-19T14:24:05Z day: '26' department: - _id: LaEr doi: 10.1142/s2010326319500096 ec_funded: 1 external_id: arxiv: - '1802.05175' isi: - '000477677200002' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1802.05175 month: '09' oa: 1 oa_version: Preprint project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: 'Random matrices: Theory and applications' publication_identifier: eissn: - 2010-3271 issn: - 2010-3263 publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: Bounds on the norm of Wigner-type random matrices type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2018' ... --- _id: '1012' abstract: - lang: eng 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. 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: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: 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 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 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. 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. ista: Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298. 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. date_created: 2018-12-11T11:49:41Z date_published: 2018-05-18T00:00:00Z date_updated: 2023-09-22T09:44:21Z day: '18' department: - _id: LaEr doi: 10.1093/imrn/rnw330 ec_funded: 1 external_id: arxiv: - '1608.05163' isi: - '000441668300009' intvolume: ' 2018' isi: 1 issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1608.05163 month: '05' oa: 1 oa_version: Preprint page: 3255-3298 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: International Mathematics Research Notices publication_identifier: issn: - '10737928' publication_status: published publisher: Oxford University Press publist_id: '6383' quality_controlled: '1' related_material: record: - id: '6179' relation: dissertation_contains status: public scopus_import: '1' status: public title: Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 2018 year: '2018' ... --- _id: '70' abstract: - lang: eng 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. article_processing_charge: No article_type: original author: - first_name: Peter full_name: Nejjar, Peter id: 4BF426E2-F248-11E8-B48F-1D18A9856A87 last_name: Nejjar citation: 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 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 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. 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. 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. 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. short: P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334. date_created: 2018-12-11T11:44:28Z date_published: 2018-10-01T00:00:00Z date_updated: 2023-10-10T13:11:29Z day: '01' ddc: - '510' department: - _id: LaEr - _id: JaMa doi: 10.30757/ALEA.v15-49 ec_funded: 1 external_id: arxiv: - '1705.08836' isi: - '000460475800022' file: - access_level: open_access checksum: 2ded46aa284a836a8cbb34133a64f1cb content_type: application/pdf creator: kschuh date_created: 2019-02-14T09:44:10Z date_updated: 2020-07-14T12:47:46Z file_id: '5981' file_name: 2018_ALEA_Nejjar.pdf file_size: 394851 relation: main_file file_date_updated: 2020-07-14T12:47:46Z has_accepted_license: '1' intvolume: ' 15' isi: 1 issue: '2' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1311-1334 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Latin American Journal of Probability and Mathematical Statistics publication_identifier: issn: - 1980-0436 publication_status: published publisher: Instituto Nacional de Matematica Pura e Aplicada quality_controlled: '1' scopus_import: '1' status: public title: Transition to shocks in TASEP and decoupling of last passage times type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2018' ... --- _id: '284' 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." 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). article_processing_charge: No article_type: original author: - first_name: Daniel full_name: Virosztek, Daniel id: 48DB45DA-F248-11E8-B48F-1D18A9856A87 last_name: Virosztek orcid: 0000-0003-1109-5511 citation: 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 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. 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. 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. short: D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80. date_created: 2018-12-11T11:45:36Z date_published: 2018-06-04T00:00:00Z date_updated: 2023-10-16T10:29:22Z day: '04' department: - _id: LaEr doi: 10.14232/actasm-018-753-y ec_funded: 1 external_id: arxiv: - '1802.03305' intvolume: ' 84' issue: 1-2 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1802.03305 month: '06' oa: 1 oa_version: Preprint page: 65 - 80 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Acta Scientiarum Mathematicarum publication_identifier: eissn: - 2064-8316 issn: - 0001-6969 publication_status: published publisher: Springer Nature publist_id: '7615' quality_controlled: '1' scopus_import: '1' status: public title: Maps on probability measures preserving certain distances - a survey and some new results type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 84 year: '2018' ...